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Confidence bands are used to estimate the likely range of the true parameter, whereas prediction bands provide an idea of the possible values of the parameter after applying a regression model. This study proposes an equation to construct confidence and prediction bands applicable to any linear or nonlinear chemometric regression model; that is, statistical methods used in analytical chemistry to establish relationships between two or more variables. The proposed equation is developed and presented as a useful tool to represent the uncertainty in estimates based on a set of data in chemical measurements. Once the set of data is adjusted as a regression model (linear, polynomial, or multivariable), the proposed equation can be used to construct confidence and prediction bands based on the adjustment equation. The proposed equation operates if the adjustment equation is continuous and derivable. The plot bands on any regression model provide a solid understanding of uncertainty assessment and have the advantage of total control and independence of algorithms and numeral approximations. [ABSTRACT FROM AUTHOR]

In this paper we give a quantitative analysis of an explicit iteration method due to C.E. Chidume for the approximation of a zero of an m-accretive operator A : X → 2 X in Banach spaces which does not involve the computation of the resolvent of A. [ABSTRACT FROM AUTHOR]

The meta-analysis of P-values is a widely used method in integrating information from multiple studies, and much research has focused on combining P-values. Among the established approaches, Fisher's test may be the most popular one. Many studies have been devoted to extending or modifying Fisher's statistic. For example, Lancaster's variation of Fisher's method may outperform the weighted Z-test and recently has drawn noteworthy attention. In this study, we first extend Lancaster's statistic by incorporating a weighting scheme. An approximation and an algorithm that are suitable for use under both independence and dependence assumptions are proposed for calculating the distribution of the weighted Lancaster statistic. The relationships between this method and existing ones are discussed. An application of the main results to a linkage test method in human gene mapping is then provided to show its use. [ABSTRACT FROM AUTHOR]

Cluster failure time data are commonly encountered in survival analysis due to unobservable factors such as shared environmental conditions and genetic similarity. In such cases, careful attention needs to be paid to the correlation among the subjects within the same cluster. In addition, some diseases are curable due to the advancement of modern medical techniques. In this paper, we extend the frailty model based on Birnbaum–Saunders frailty distribution to incorporate the cure proportion. In addition, the marginal likelihood approach using Monte Carlo approximation and Expectation-Maximization algorithm are also developed for the determination of the maximum likelihood estimates of the parameters of the proposed model. An extensive simulation study is carried out to evaluate the performance of the proposed model and the methods of inference. Finally, the proposed model is applied to a real data set to analyse the effect of allogeneic and autologous bone marrow transplant treatment on acute lymphoblastic leukemia patients. [ABSTRACT FROM AUTHOR]

In this paper, we propose and investigate a new kernel regression estimators based on the two-time-scale stochastic approximation algorithm in the case of independent functional data. We study the properties of the proposed recursive estimators and compare them with the recursive estimators based on single-time-scale stochastic algorithm proposed by Slaoui and to the non-recursive estimator proposed by Slaoui. It turns out that, with an adequate choice of the parameters, the proposed two-time-scale estimators perform better than the recursive estimators constructed using single-time-scale stochastic algorithm. We corroborate these theoretical results through some simulations and two real datasets. [ABSTRACT FROM AUTHOR]

In this paper we establish some approximation versions of the classical Dinkelbach algorithm for nonlinear fractional optimization problems in Banach spaces. We start by examining what occurs if at any step of the algorithm, the generated point desired to be a minimizer can only be determined with a given error. Next we assume that the step error tends to zero as the algorithm advances. The last version of the algorithm we present is making use of Ekeland's variational principle for generating the sequence of minimizer-like points. In the final part of the article we deliver some results in order to achieve a Palais-Smale type compactness condition that guarantees the convergence of our Dinkelbach-Ekeland algorithm. [ABSTRACT FROM AUTHOR]

In this study, we present a general framework of outer approximation algorithms to solve convex vector optimization problems, in which the Pascoletti-Serafini (PS) scalarization is solved iteratively. This scalarization finds the minimum 'distance' from a reference point, which is usually taken as a vertex of the current outer approximation, to the upper image through a given direction. We propose efficient methods to select the parameters (the reference point and direction vector) of the PS scalarization and analyse the effects of these on the overall performance of the algorithm. Different from the existing vertex selection rules from the literature, the proposed methods do not require solving additional single-objective optimization problems. Using some test problems, we conduct an extensive computational study where three different measures are set as the stopping criteria: the approximation error, the runtime, and the cardinality of the solution set. We observe that the proposed variants have satisfactory results, especially in terms of runtime compared to the existing variants from the literature. [ABSTRACT FROM AUTHOR]

Bayesian structure learning in Gaussian graphical models is often done by search algorithms over the graph space.The conjugate prior for the precision matrix satisfying graphical constraints is the well-known G-Wishart.With this prior, the transition probabilities in the search algorithms necessitate evaluating the ratios of the prior normalizing constants of G-Wishart.In moderate to high-dimensions, this ratio is often approximated by using sampling-based methods as computationally expensive updates in the search algorithm.Calculating this ratio so far has been a major computational bottleneck.We overcome this issue by representing a search algorithm in which the ratio of normalizing constants is carried out by an explicit closed-form approximation.Using this approximation within our search algorithm yields significant improvement in the scalability of structure learning without sacrificing structure learning accuracy.We study the conditions under which the approximation is valid.We also evaluate the efficacy of our method with simulation studies.We show that the new search algorithm with our approximation outperforms state-of-the-art methods in both computational efficiency and accuracy.The implementation of our work is available in the R package BDgraph. [ABSTRACT FROM AUTHOR]

Selecting appropriate inputs for systems described by complex networks is an important but difficult problem that largely remains open in the field of control of networks. Recent work has proposed two methods for energy efficient input selection; a gradient-based heuristic and a greedy approximation algorithm. We propose here an alternative method for input selection based on the analytic solution of the controllability Gramian of the 'balloon graph', a special model graph that captures the role of both distance and redundant paths between a driver node and a target node. The method presented is especially applicable for large networks where one is interested in controlling only a small number of outputs, or target nodes, for which current methods may not be practical because they require computing a typically very ill-conditioned matrix, called the controllability Gramian. Our method produces comparable results to the previous methods while being more computational efficient. [ABSTRACT FROM AUTHOR]

Set-valued optimization using the set approach is a research topic of high interest due to its practical relevance and numerous interdependencies to other fields of optimization. However, it is a very difficult task to solve these optimization problems even for specific cases. In this paper, we study set-valued optimization problems and develop a multiobjective optimization problem that is strongly related to it. We prove that the set of weakly minimal solutions of this subproblem is closely related to the set of weakly minimal elements of the set-valued optimization problem and that these sets can get arbitrarily close in a certain sense. Subsequently, we introduce a concept of approximations of the solution set of the set-valued optimization problem. We define a quality measure in the image space that can be used to compare finite approximations of this kind and outline a procedure to enhance a given approximation. We conclude the paper with some numerical examples. [ABSTRACT FROM AUTHOR]

Sliced inverse regression (SIR) is a recommended method to identify and estimate the central dimension reduction (CDR) subspace. CDR subspace is at the base to describe the conditional distribution of the response Y given a d-dimensional predictor vector X. To estimate this space, two versions are very popular: the slice version and the kernel version. A recursive method of the slice version has already been the subject of a systematic study. In this paper, we propose to study the kernel version. It's a recursive method based on a stochastic approximation algorithm of the kernel version. The asymptotic normality of the proposed estimator is also proved. A simulation study that not only shows the good numerical performance of the proposed estimate and which also allows to evaluate its performance with respect to existing methods is presented. A real dataset is also used to illustrate the approach. [ABSTRACT FROM AUTHOR]

This study addresses the scheduling problem of two identical parallel machines with the objective of minimizing the total completion time under the machine availability constraints. To the best of our knowledge, this study is the first to develop a fully polynomial-time approximation scheme (FPTAS), a solution method which has been neglected in past studies, to solve the studied problem. The FPTAS, which is based on a dynamic programming algorithm is developed by applying a trimming-the-state-space approach. Theoretical proofs of the error bound and the time complexity for the proposed FPTAS are also provided. The computational results indicate that the proposed FPTAS performs more efficiently than a dynamic programming algorithm in terms of both run time and problem size. The error bound of the FPTAS is demonstrated to be within the pre-specified error bound. [ABSTRACT FROM AUTHOR]

Pareto frontiers of bicriteria continuous convex problems can be efficiently computed and optimal theoretical performance bounds have been established. In the case of bicriteria mixed-integer problems, the approximation of the Pareto frontier becomes, however, significantly harder. In this paper, we propose a new algorithm for approximating the Pareto frontier of bicriteria mixed-integer programs with convex constraints. Such Pareto frontiers are composed of patches of solutions with shared assignments for the discrete variables. By adaptively creating such a patchwork, our algorithm is able to create approximations that converge quickly to the true Pareto frontier. As a quality measure, we use the difference in hypervolume between the approximation and the true Pareto frontier. At least a certain number of patches is required to obtain an approximation with a given quality. This patch complexity gives a lower bound on the number of required computations. We show that our algorithm performs a number of optimization steps that are of a similar order as this lower bound. We provide an efficient MIP-based implementation of this algorithm. The efficiency of our algorithm is illustrated with numerical results showing that our algorithm has a strong theoretical performance guarantee while being competitive with other state-of-the-art approaches in practice. [ABSTRACT FROM AUTHOR]

In this paper, we consider an extension of the generalized class of recursive regression estimators to the case of strong mixing data. Then, we study the properties of these estimators and compare them with the well known Nadaraya-Watson estimator. The Bias, variance and Mean Integrated Square Error are computed explicitly. Using a selected bandwidth and a special stepsize, we showed that the proposed recursive estimators allowed us to obtain quite better results compared to the non-recursive regression estimator under α-mixing condition in terms of estimation error and much better in terms of computational costs. [ABSTRACT FROM AUTHOR]

This paper introduces a general area-level model-based formulation to small area estimation based on generalized linear mixed models. By applying an optimization algorithm to the Laplace approximation of the likelihood, the maximum likelihood estimators of the model parameters are calculated. Empirical best predictors of small area quantities are derived and the corresponding mean squared errors are estimated by parametric bootstrap. Some simulation experiments are carried out to study the behavior of the fitting algorithm, the small area predictors and the estimators of the mean squared errors. By using data of the Spanish living condition survey of 2008, an application to the estimation of average annual net incomes in Spanish provinces by sex is given. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel dual active-set algorithm that is based on proximal gradient and semi-smooth Newton iterations for the sparse approximation of correlation matrices in the Frobenius norm. A new dual formulation with upper and lower bounds is derived. To solve the dual, the proximal gradient method is developed to guarantee global convergence. Also, it provides information to estimate active/inactive constraints. Then, the semi-smooth Newton method is applied to accelerate the convergence of the proximal gradient method, which is the key ingredient of our algorithm. It is shown that the proposed algorithm for the dual is globally convergent under certain conditions. Some preliminary numerical results are given to illustrate the effectiveness of our algorithm on synthetic and real data sets. [ABSTRACT FROM AUTHOR]

In this work, we propose integral global optimality conditions for multiobjective problems not necessarily differentiable. The integral characterization, already known for single objective problems, are extended to multiobjective problems by weighted sum and Chebyshev weighted scalarizations. Using this last scalarization, we propose an algorithm for obtaining an approximation of the weak Pareto front whose effectiveness is illustrated by solving a collection of multiobjective test problems. [ABSTRACT FROM AUTHOR]

Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral clustering using randomized sketching algorithms from a statistical perspective, where we typically assume the network data are generated from a stochastic block model that is not necessarily of full rank. To do this, we first use the recently developed sketching algorithms to obtain two randomized spectral clustering algorithms, namely, the random projection-based and the random sampling-based spectral clustering. Then we study the theoretical bounds of the resulting algorithms in terms of the approximation error for the population adjacency matrix, the misclassification error, and the estimation error for the link probability matrix. It turns out that, under mild conditions, the randomized spectral clustering algorithms lead to the same theoretical bounds as those of the original spectral clustering algorithm. We also extend the results to degree-corrected stochastic block models. Numerical experiments support our theoretical findings and show the efficiency of randomized methods. A new R package called Rclust is developed and made available to the public. for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of the regression estimation near the edges under censoring. For this purpose, we consider a new recursive estimator based on the stochastic approximation algorithm and Bernstein polynomials of the regression function when the response random variable is subject to random right censoring. We give the central limit theorem and the strong pointwise convergence rate for our proposed nonparametric recursive estimators under some mild conditions. Finally, we provide pointwise moderate deviation principles (MDP) for the proposed estimators. We corroborate these theoretical results through simulations as well as the analysis of a real data set. [ABSTRACT FROM AUTHOR]

The correlational structure of a set of variables is often conveniently described by the pairwise partial correlations as they contain the same information as the Pearson correlations with the advantage of straightforward identifications of conditional linear independence. For mathematical convenience, multiple matrix representations of the pairwise partial correlations exist in the literature but their properties have not been investigated thoroughly. In this paper, we derive necessary and sufficient conditions for the eigenvalues of differently defined partial correlation matrices so that the correlation structure is a valid one. Equipped with these conditions, we will then emphasize the intricacies of algorithmic generations of correlation structures via partial correlation matrices. Furthermore, we examine the space of valid partial correlation structures and juxtapose it with the space of valid Pearson correlation structures. As these spaces turn out to be equal in volume for every dimension and equivalent with respect to rotation, a simple formula allows the creation of valid partial correlation matrices by the use of current algorithms for the generation and approximation of correlation matrices. Lastly, we derive simple conditions on the partial correlations for frequently assumed sparse structures. [ABSTRACT FROM AUTHOR]

We develop a real-time anomaly detection method for directed activity on large, sparse networks. We model the propensity for future activity using a dynamic logistic model with interaction terms for sender- and receiver-specific latent factors in addition to sender- and receiver-specific popularity scores; deviations from this underlying model constitute potential anomalies. Latent nodal attributes are estimated via a variational Bayesian approach and may change over time, representing natural shifts in network activity. Estimation is augmented with a case-control approximation to take advantage of the sparsity of the network and reduces computational complexity from O (N 2) to O(E), where N is the number of nodes and E is the number of observed edges. We run our algorithm on network event records collected from an enterprise network of over 25,000 computers and are able to identify a red team attack with half the detection rate required of the model without latent interaction terms. [ABSTRACT FROM AUTHOR]

In order to enhance the calculation efficiency of steady-state incompressible fluid flow, based on the existing IDEAL (i.e. the inner doubly iterative efficient algorithm for linked equations) algorithm, a novel segregated pressure-based algorithm (named as IDEALC) has been developed in this paper. The novel algorithm inherits the superiorities of the original IDEAL algorithm and at the same time improves its potential shortcomings. The specific promotions of the IDEALC algorithm consist of three aspects, including the first approximation of the SIMPLE algorithm, the approach to solving the momentum equation and the second approximation of the SIMPLE algorithm. Detailed comparisons between the IDEAL and the IDEALC algorithms are carried out by three numerical experiments on structured collocated grids. The numerical results demonstrate that the IDEALC algorithm can accurately predict the information of the flow field and has substantial advantages over the IDEAL algorithm in terms of the efficiency because of the consistent property of the former. The superiority of the IDEALC algorithm over the IDEAL algorithm is especially remarkable when the time step multiplier gets a moderate value. [ABSTRACT FROM AUTHOR]

A new algorithm for the approximation and simulation of twofold iterated stochastic integrals together with the corresponding Lévy areas driven by a multidimensional Brownian motion is proposed. The algorithm is based on a truncated Fourier series approach. However, the approximation of the remainder terms differs from the approach considered by Wiktorsson (2001). As the main advantage, the presented algorithm makes use of a diagonal covariance matrix for the approximation of one part of the remainder term and has a higher accuracy due to an exact approximation of the other part of the remainder. This results in a significant reduction of the computational cost compared to, e.g., the algorithm introduced by Wiktorsson. Convergence in L p (Ω) -norm with p ≥ 2 for the approximations calculated with the new algorithm as well as for approximations calculated by the basic truncated Fourier series algorithm is proved and the efficiency of the new algorithm is analyzed. [ABSTRACT FROM AUTHOR]

Nonlinear equations are usually solved numerically. However, approximated analytical solutions of nonlinear equations are useful as an initial iteration point for numerical methods. Furthermore, these analytical approximations are sometimes quite close to the actual root. In order to teach at undergraduate level how to perform this kind of approximation, we propose problem-based learning with some nonlinear equations extracted from Applied Sciences. We also present a simple method to analytically solve nonlinear equations which are not solvable by standard computer algebra solvers. [ABSTRACT FROM AUTHOR]

In this paper, the application of randomized projection functional algorithms for numerical approximation of solutions of Fredholm equations of the second kind is discussed. Special attention is paid to the problems of numerical stability of the used orthonormal functional bases. The numerical instability of the randomized projection functional algorithm is noticed for the simple test one-dimensional equation and for the Hermite orthonormal basis. [ABSTRACT FROM AUTHOR]

A rough volatility model contains a stochastic Volterra integral with a weakly singular kernel. The classical Euler-Maruyama algorithm is not very efficient for simulating this kind of model because one needs to keep records of all the past path-values and thus the computational complexity is too large. This paper develops a fast two-step iteration algorithm using an approximation of the weakly singular kernel with a sum of exponential functions. Compared to the Euler-Maruyama algorithm, the complexity of the fast algorithm is reduced from O (N 2) to O (N log ⁡ N) or O (N log 2 ⁡ N) for simulating one path, where N is the number of time steps. Further, the fast algorithm is developed to simulate rough Heston models with (or without) regime switching, and multi-factor approximation algorithms are also studied and compared. The convergence rates of the Euler-Maruyama algorithm and the fast algorithm are proved. A number of numerical examples are carried out to confirm the high efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The objective is to study the existence and uniqueness questions for a nonlinear Volterra-Fredholm integro-differential equation, then, develop a numerical approach using the Nyström method coupled with successive approximations algorithm. A numerical example is presented to examine the efficiency of the proposed method according to the existence and uniqueness conditions. [ABSTRACT FROM AUTHOR]

For a graph G = (V , E) , a double Roman dominating function (DRDF) is a function f : V → { 0 , 1 , 2 , 3 } having the property that if f (v) = 0 , then vertex v must have at least two neighbours assigned 2 under f or at least one neighbour u with f (u) = 3 , and if f (v) = 1 , then vertex v must have at least one neighbour u with f (u) ≥ 2. In this paper, we consider the double Roman domination problem, which is an optimization problem of finding the DRDF f such that ∑ v ∈ V f (v) is minimum. We propose five integer linear programming (ILP) formulations and one mixed integer linear programming formulation with polynomial number of constraints for this problem. Some additional valid inequalities and bounds are also proposed for some of these formulations. Further, we prove that the first four models indeed solve the double Roman domination problem, and the last two models are equivalent to the others regardless of the variable relaxation or usage of a smaller number of constraints and variables. Additionally, we use one ILP formulation to give an H (2 (Δ + 1)) -approximation algorithm. All proposed formulations and approximation algorithm are evaluated on randomly generated graphs to compare the performance. [ABSTRACT FROM AUTHOR]

The covariance matrix reconstruction based robust adaptive beamforming (RAB) methods overcome the performance degradation due to the imprecise knowledge of the steering vector and the covariance matrix. However, high complexity limits the application of them. In this paper, we proposed a new RAB method based on interference plus noise covariance (INC) matrix reconstruction and desired signal steering vector estimation. In this method, nominal interference steering vectors are estimated by the Capon spatial spectrum, as well as noise power. Subsequently, the iterative mismatch approximation algorithm based on maximizing the beamformer output power is proposed to estimate all the incident signal steering vectors and powers, and the INC matrix is reconstructed. Finally, the beamformer is determined by the estimated INC matrix and desired signal steering vector. Simulation results indicate that the proposed method obtains better performance than other existed methods at both the high signal to noise ratio (SNR) and the complexity. [ABSTRACT FROM AUTHOR]

In this article, we aim to solve Bayesian Risk Optimization (BRO), which is a recently proposed framework that formulates simulation optimization under input uncertainty. In order to efficiently solve the BRO problem, we derive nested stochastic gradient estimators and propose corresponding stochastic approximation algorithms. We show that our gradient estimators are asymptotically unbiased and consistent, and that the algorithms converge asymptotically. We demonstrate the empirical performance of the algorithms on a two-sided market model. Our estimators are of independent interest in extending the literature of stochastic gradient estimation to the case of nested risk measures. [ABSTRACT FROM AUTHOR]

In this paper, we propose two kernel distribution estimators based on a data transformation. We study the properties of these estimators and we compare them with two conventional estimators. It appears that with an appropriate choice of the parameters of the two proposed estimators, the convergence rate of two estimators will be faster than that of the two conventional estimators and the Mean Integrated Square Error will be smaller than the two conventional estimators. We corroborate these theoretical results through simulations as well as a real data set. [ABSTRACT FROM AUTHOR]

We consider two-machine routing open shop problem on a tree. In this problem, a transportation network with a tree-like structure is given, and each node contains some jobs to be processed by two mobile machines. Machines are initially located in the predefined node called the depot, have to traverse the network to perform their operations on each job (and each job has to be processed by both machines in arbitrary order), and machines have to return to the depot after performing all the operations. The goal is to construct a feasible schedule for machines to process all the jobs and to return to the depot in shortest time possible. This problem is known to be NP-hard even in the case when the transportation network consists of just two nodes. We propose an instance reduction procedure which allows to transform any instance of the problem to a simplified instance on a chain with limited number of jobs. The reduction considered preserves the standard lower bound on the optimum. We describe four possible outcomes of this procedure and prove that in three of them the initial instance can be solved to the optimum in linear time, thus introducing a wide polynomially solvable subclass of the problem considered. Our research can be used as a foundation to construct efficient approximation algorithms for the two-machine routing open shop on a tree. [ABSTRACT FROM AUTHOR]

This paper presents a generic framework for the design and comparison of polynomial-time approximation algorithms for MINIMUM STAR BICOLORING. This generic framework is parameterized by algorithms which produce sequences of distance- 2 independent sets. As our main technical result we show that, when the parameterized algorithm produces sequences of distance- 2 independent sets that remove at least Ω (n ϵ) edges during each step, the generic framework produces a polynomial-time approximation algorithm for MINIMUM STAR BICOLORING that is always at least O (n 1 − ϵ / (1 + ϵ) ) of optimal. Under the generic framework, we model two algorithms for MINIMUM STAR BICOLORING from the literature: Complete Direct Cover (CDC) [Hossain and Steihaug, Computing a sparse Jacobian matrix by rows and columns, Optim. Methods Softw. 10 (1998), pp. 33–48] and ASBC [Juedes and Jones, Coloring Jacobians revisited: A new algorithm for star and acyclic bicoloring, Optim. Methods Softw. 27(1–3) (2012), pp. 295–309]. We apply our main result to show approximation upper bounds of O (n 3 / 4) and O (n 2 / 3) , respectively, for these two algorithms. Our approximation upper bound for CDC is the first known approximation analysis for this algorithm. In addition to modelling CDC and ASBC, we use the generic framework to build and analyze three new O (n 2 / 3) approximation algorithms for MINIMUM STAR BICOLORING: MAX-NEIGHBORHOOD, MAX-RATIO c , and LOCAL-SEARCH-k. [ABSTRACT FROM AUTHOR]

We consider a conflict-free minimum latency data aggregation problem that occurs in different wireless networks. Given a network that is presented as an undirected graph with one selected vertex (a sink), the goal is to find a spanning aggregation tree rooted in the sink and to define a conflict-free aggregation minimum length schedule along the arcs of the tree directed to the sink. Herewith, at the same time slot, each element of the network can either send or receive at most one message. Only one message should be sent by each network element during the whole aggregation session, and the conflicts caused by signal interference should be excluded. This problem is NP-hard and remains NP-hard even in the case when the aggregation tree is given. Therefore, the development of efficient approximation algorithms is very important for this problem. In this paper, we present new heuristic algorithms based on genetic local search and variable neighbourhood search metaheuristics. We conducted an extensive simulation that demonstrates the superiority of our algorithms compared with the best of the previous approaches. [ABSTRACT FROM AUTHOR]

Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined parts: single-objective linear optimization on one hand, and a combinatorial part closely related to vertex enumeration on the other. Their separation provides a deeper insight into Benson's algorithm, and points toward a dual approach. Two skeletal algorithms are defined which focus on the combinatorial part. Using different single-objective optimization problems yields different algorithms, such as a sequential convex hull algorithm, another version of Benson's algorithm with the theoretically best possible iteration count, and the dual algorithm of Ehrgott et al. [A dual variant of Benson's 'outer approximation algorithm' for multiple objective linear programming. J Glob Optim. 2012;52:757–778]. The implemented version is well suited to handle highly degenerate problems where there are many linear dependencies among the constraints. On problems with 10 or more objectives, it shows a significant increase in efficiency compared to Bensolve – due to the reduced number of iterations and the improved combinatorial handling. [ABSTRACT FROM AUTHOR]

In an application of map labelling to air-traffic control, labels should be placed with as few overlaps as possible since labels include important information about airplanes. Motivated by this application, de Berg and Gerrits (Comput. Geom. 2012) proposed a problem of maximizing the number of free labels (i.e. labels not intersecting with any other label) and developed approximation algorithms for their problem under various label-placement models. In this paper, we propose an alternative problem of minimizing a degree of overlap at a point. Specifically, the objective of this problem is to minimize the maximum of λ (p) over p ∈ R 2 , where λ (p) is defined as the sum of weights of labels that overlap with a point p. We develop a 4-approximation algorithm by LP-rounding under the 4-position model. We also investigate the case when labels are rectangles with bounded height/length ratios. [ABSTRACT FROM AUTHOR]

In this paper, based on hybrid censored sample from a two parameter exponentiated half logistic distribution, we consider the problem of estimating the unknown parameters using frequentist and Bayesian approaches. Expectation-Maximization, Lindley's approximation and Metropolis-Hastings algorithms are used for obtaining point estimators and corresponding confidence intervals for the shape and scale parameters involved in the underlying model. Data analyses involving the survival times of patients suffering from cancer diseases and treated radiotherapy and/or chemotherapy have been performed. Finally, numerical simulation study was conducted to assess the performances of the so developed methods and conclusions on our findings are reported. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of vector scheduling with rejection on two identical parallel machines, where the objective is to minimize the sum of maximum load over all dimensions and machines and the total penalty cost. We present a 3-approximation algorithm and a 2.54-approximation algorithm based randomized rounding for the general case. When the number of dimensions is fixed, we design a fully polynomial time approximation scheme based on dynamic programming. Finally, we design an online algorithm with competitive ratio 1.62d, where d is the number of dimensions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a relative recursive regression estimator for censored data defined by the stochastic approximation algorithm to deal with the presence of outliers or when the response is usually positive. We give the central limit theorem and the strong pointwise convergence rate for our proposed nonparametric relative recursive estimators under some mild conditions. We finally developed a second generation plug-in bandwidth selection procedure. [ABSTRACT FROM AUTHOR]

This paper considers a new model in search theory to find a randomly located target in the 3-dimensional space. An approximation algorithm that facilitates searching procedures for searchers or robots is presented. The expected time to detect the target is also proved. The statistical analysis by calculating the optimal search strategy which minimizes the time to detect the target, assuming trivariate standard normal distribution is provided, and the technique by flowcharts is designed as well. The effectiveness of this strategy is illustrated by introducing an application from real world. [ABSTRACT FROM AUTHOR]

In this article we propose an automatic selection of the bandwidth of the recursive kernel density estimators for spatial data defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the MWISE (Mean Weighted Integrated Squared Error), the recursive estimator will be quite similar to the nonrecursive one in terms of estimation error and much better in terms of computational costs. In addition, we obtain the central limit theorem for the nonparametric recursive density estimator under some mild conditions. [ABSTRACT FROM AUTHOR]

This article mainly studies the nonuniform and semi-average sampling of time-varying shift-invariant signals living in a mixed Lebesgue space L p , q (R d + 1) , under the condition that the generator φ of the shift-invariant subspace belongs to a hybrid-norm space of mixed form depending on the orders p and q. First, the sampling stability for two kinds of semi-average sampling functionals is established. Then, we give the corresponding iterative approximation projection algorithms with exponential convergence for recovering the time-based shift-invariant signals from the semi-average samples. [ABSTRACT FROM AUTHOR]

This article considers a new variation of the online interval scheduling problem, which consists of scheduling C-benevolent jobs on multiple heterogeneous machines with different positive weights. The reward for completing a job assigned to a machine is given by the product of the job value and the machine weight. The objective of this scheduling problem is to maximize the total reward for completed jobs. Two classes of approximation algorithms are analyzed, Cooperative Greedy algorithms and Prioritized Greedy algorithms, with competitive ratios provided. We show that when the weight ratios between machines are small, the Cooperative Greedy algorithm outperforms the Prioritized Greedy algorithm. As the weight ratios increase, the Prioritized Greedy algorithm outperforms the Cooperative Greedy algorithm. Moreover, as the weight ratios approach infinity, the competitive ratio of the Prioritized Greedy algorithm approaches four. We also provide a lower bound of 3/2 and 9/7 for the competitive ratio of any deterministic algorithm for scheduling C-benevolent jobs on two and three machines with arbitrary weights, respectively. [ABSTRACT FROM AUTHOR]

This article studies how to identify strategies for mitigating cyber-infrastructure vulnerabilities. We propose an optimization framework that prioritizes the investment in security mitigations to maximize the coverage of vulnerabilities. We use multiple coverage to reflect the implementation of a layered defense, and we consider the possibility of coverage failure to address the uncertainty in the effectiveness of some mitigations. Budgeted Maximum Multiple Coverage (BMMC) problems are formulated, and we demonstrate that the problems are submodular maximization problems subject to a knapsack constraint. Other variants of the problem are formulated given different possible requirements for selecting mitigations, including unit cost cardinality constraints and group cardinality constraints. We design greedy approximation algorithms for identifying near-optimal solutions to the models. We demonstrate an optimal (1–1/e)-approximation ratio for BMMC and a variation of BMMC that considers the possibility of coverage failure, and a 1/2-approximation ratio for a variation of BMMC that uses a cardinality constraint and group cardinality constraints. The computational study suggests that our models yield robust solutions that use a layered defense and provide an effective mechanism to hedge against the risk of possible coverage failure. We also find that the approximation algorithms efficiently identify near-optimal solutions, and that a Benders branch-and-cut algorithm we propose can find provably optimal solutions to the vast majority of our test instances within an hour for the variations of the proposed models that consider coverage failures. [ABSTRACT FROM AUTHOR]

A randomised algorithm is proposed for computing globally optimal static-output-feedbacks for large-scale systems. The algorithm is based on the Ray-Shooting Method and involves some heuristics to accelerate the search. We also improve the basic Ray-Shooting Algorithm and make the search in the controller parameter-space (which generally, is much more smaller than the certificate parameter-space), thus enabling its efficient use for large-scale systems. [ABSTRACT FROM AUTHOR]

This article presents an improved genetic algorithm with two-level approximation (GATA) to optimize the distribution and size of stiffeners simultaneously. A novel optimization model of stiffeners, including two kinds of design variables, is established. The first level approximation problem transforms the original implicit problem to an explicit problem which involves the topology and size variables. Then, a genetic algorithm (GA) addresses the mixed variables. The individuals in the GA are coded by topology variables, and when calculating an individual's fitness, the second level approximation problem is embedded to optimize the size variables. Considering the stiffeners' optimization, several aspects of the initial GATA are updated, including the relationship between two kinds of variables, the weight and its sensitivity calculation and the GA strategy, to optimize the stiffeners' size and distribution simultaneously. Numerical examples show that the improved GATA is effective in optimizing the stiffened shells' topology and size variables simultaneously. [ABSTRACT FROM AUTHOR]

This article addresses permutation flowshop scheduling problems with simple linear deterioration. The objectives are to minimize logarithm of the makespan, total logarithm of the completion time, total weighted logarithm of the completion time, and the sum of the quadratic job logarithms of the completion times. Approximation algorithms and their worst-case bounds are presented and analysed. Branch-and-bound algorithms are also proposed to solve the problems optimally. Computational experiments are performed to illustrate the algorithms. [ABSTRACT FROM AUTHOR]

Observational or nonrandomized studies of treatment effects are often constructed with the aid of polynomial-time algorithms that optimally form matched treatment-control pairs or matched sets. Because each observational comparison may potentially be affected by bias, investigators often reinforce a single comparison with an additional comparison that is unlikely to be affected by the same biases, for instance using multiple control groups or evidence factors or control + instrument designs. Use of two comparisons affected by different biases may detect bias if the two comparisons disagree, or may show that two comparisons with different weakness concur in their conclusions. Even this simplest addition—a second comparison—creates design problems without polynomial-time solutions. Faced with a problem that no polynomial-time algorithm can solve, a so-called approximation algorithm is a type of compromise: it provides a solution in polynomial time that is provably not much worse than the unattainable optimal solution. Building upon existing techniques for related problems in operations research, we develop an approximation algorithm for minimum distance matching with near-fine balance for three comparison groups. This algorithm is a practical approach to most observational designs that add a second comparison. The method is applied to an observational study of the effects of side airbags on injury severity in the U.S. Fatality Analysis Reporting System. For many car makes and models, side airbags were initially unavailable, then later available as optional equipment for an additional fee, then still later provided as standard equipment. Within sets matched for make and model of car, for safety belt use, for direction of impact, and other covariates, we compare crashes in these three periods, where each comparison has different limitations. The method is implemented in the R package approxmatch, whose example reproduces some of the calculations. for this article are available online. [ABSTRACT FROM AUTHOR]

We present a method to solve constrained convex stochastic optimization problems when the objective is a finite sum of convex functions. Our method is based on Incremental Stochastic Subgradient Algorithms and String-Averaging techniques, with an assumption that the subgradient directions are affected by random errors in each iteration. Our analysis allows the method to perform approximate projections onto the feasible set in each iteration. We provide convergence results for the case where a diminishing step-size rule is used. We test our method in a large set of random instances of a stochastic convex programming problem and we compare its performance with the robust mirror descent stochastic approximation algorithm proposed in Nemirovski et al. (Robust stochastic approximation approach to stochastic programming, SIAM J Optim 19 (2009), pp. 15741609). [ABSTRACT FROM AUTHOR]

Routh Approximation is believed to witness tremendous usage in deriving the reduced models from their higher equivalents. Order reduction is a critical field of interest for researchers or control engineers dealing with practical and physical systems of higher order. Reason for the popularity of Routh Approximation among other reduction methodologies is its strength of computational simplicity, ease of access and the promise to retain the model stability. This paper accomplishes a survey of the available Routh Approximation algorithms in their varied configuration since five decades. Last survey report based on Routh Approximation was cited in late seventies as discussed in the paper. One prime reason for the outcome of this paper is the problem met by the authors during their own work for analysing varied configuration of Routh Approximation for order reduction. Many times, the arrangement, stated or performed, seemed to be already in existence. Thus, the paper would be helpful to the researchers working in the area of order reduction and have prime focus on the utility of Routh Approximation. [ABSTRACT FROM AUTHOR]