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In this paper the problem of maximizing vertex-degree function index H f ( G ) for trees and unicyclic graphs G of order n and independence number s is solved for strictly convex functions f ( x ) . In the case of unicyclic graphs f ( x ) must also satisfy strict inequality f ( 4 ) + 3 f ( 2 ) > 3 f ( 3 ) + f ( 1 ) . These conditions are fulfilled by general first Zagreb index 0 R α ( G ) for α > 2 , second multiplicative Zagreb index ∏ 2 ( G ) and sum lordeg index S L ( G ) . The extremal graphs are unique and they are stars or have diameter equal to three or to four. The same results are valid for the corresponding minimization problem when f ( x ) is strictly concave and the inequality is reversed.

In this article, we discuss a priori error estimates of a bubble enriched nonconforming finite element method for a linear quadratic elliptic distributed optimal control problem with integral state constraints. Therein, using the state equation we reduce the state-control constrained minimization problem to a pure state constrained minimization problem. We have obtained the optimal order (with respect to regularity) error estimates of finite element approximation in two cases: the optimal control problem with integral state constraints together with (i) integral control constraints (ii) pointwise control constraints. Numerical results are presented to confirm the theoretical findings.

Color image restoration is an ill-posed problem, and regularization is necessary. In this paper, we first formulate the color image restoration problem into a constrained minimization problem that minimizes a quadratic functional and subject to a constraint that the total variation of the color image is less than a given parameter δ. The advantages of the constrained minimization problem over the traditional unconstrained one is that the parameter δ has an obvious physical meaning and is easy to select. However solving the constrained minimization problem is generally more difficult than solving the corresponding unconstrained form. We propose an effective alternating direction method of multipliers for color image restoration by using the structure of the problem. We prove the convergence of the method in detail. Experimental results demonstrate that the proposed method is feasible and much more effective for color image restoration.

The cutwidth minimization problem (CMP) consists in determining a linear layout (i.e., a one-dimensional arrangement), of the vertices of a graph that minimizes the maximum number of edges crossing any consecutive pair of vertices. This problem has applications, for instance, in design of very large-scale integration circuits, graph drawing, and compiler design. The CMP is an NP -Hard problem and presents a challenge to exact methods and heuristics. In this study, the metaheuristic adaptive large neighborhood search is applied to the CMP. The computational experiments include 11,786 benchmark instances from four sets in the literature, and the obtained results are compared with state-of-the-art methods. The proposed method was demonstrated to be competitive, as it matched most optimal and best known results, improved some of the (not proved optimal) best known solutions, and provided the first upper bounds for unsolved instances.

In this work, we introduce a useful and efficient calculation method for solving linear fractional pantograph delay equations (FPDEs). The proposed method is primarily dependent on the least-squares approximation technique. After embedding the problem into a minimization problem, it solves the Lagrange multiplier method. The convergence analysis is theoretically proved. Finally, some numerical examples singled out to show the usefulness and capability of the suggested approach.

In this paper, we consider eigenvalue problems of a second-order measure differential equation. We first study some general theories regarding the completely continuity of eigenvalues, the variational characterizations of eigenvalues, and the oscillating properties of eigenfunctions. Then, we solve the following minimization problem: when the m-th Neumann eigenvalue is given, to find explicitly what measures will have the minimal total variation. As applications of this minimization problem, we will solve some extremal problems of eigenvalues and construct some optimal classes of non-degenerate measures for the second-order measure differential equations.

A non-fragile robust model predictive control (RMPC) is designed in the uncertain systems under bounded control signals. To this aim, a class of the nonlinear systems with additive uncertainty is considered in its general form. The RMPC synthesis could lead to the proper selection of the controller’s gains. Thus, the non-fragile RMPC design is translated into a minimization problem subjected to some constraints in terms of linear matrix inequality (LMI). Hence, the controller’s gains are computed by solving such a minimization problem. In some numerical examples, the suggested non-fragile RMPC is compared with the other methods. The simulation results demonstrate the effectiveness of the proposed RMPC in comparison with similar techniques.

This paper is aimed at the derivation of a discrete data smoothing function for the discrete Dirichlet condition in a regular grid on the surface of a spheroid. The method employed here is the local L2 seminorm minimization, through Euler Lagrange method, for the Beltrami operator. The method results in a weighted average of the surrounding points in a template based on the first order Taylor expansion of the unknown function under consideration. The coefficients of the weighted average are calculated and used to smooth the Geoid height data in Iran, derived from the EGM2008 geopotential model, Geodesy and Geodynamics, 11 (4)

In this paper, we deal with the optimization method of ridge parameters in a generalized ridge regression by minimizing a model selection criterion (MSC). The optimization methods based on minimizations of generalized C p criterion and GCV criterion are fast because the minimizers of the two criteria can be derived as closed forms. Although the methods are fast, they do not work well when the number of explanatory variables is larger than the sample size. Methods based on minimizations of other MSCs may work well even if the number of explanatory variables is larger than the sample size and are not fast because the minimizers of the MSCs have not been derived as closed forms. Even though a minimization problem of MSC cannot be solved analytically, we propose a fast optimization algorithm to minimize MSC by specifying the small number of minimizer candidates. By conducting numerical examinations, we compare performances of the optimization methods based on the minimizations of MSCs.

We consider the class of completely monotone probability mass functions (pmf) from a statistical perspective. An element in this class is known to be a mixture of geometric pmfs, a consequence of the celebrated Hausdorff Theorem. We show that the complete monotone least squares estimator exists, is strongly consistent and converges weakly to the truth at the n -rate. Furthermore, we fully describe its limit distribution as the unique solution of a well-posed minimization problem. Through a simulation study we assess the performance of the method under different scenarios.

The hydra number is a new graph parameter related to some minimization problem for Horn formulas in propositional logic. The hydra number of a graph G = ( V , E ) is the smallest number of hyperarcs of the form u v → w in a directed hypergraph H = ( V , F ) such that if u v ∈ E , then all vertices in V are reachable from { u , v } in H and if u v ⁄ ∈ E , then no other vertex apart from u and v is reachable from { u , v } . Reachability is defined by forward chaining, a standard marking procedure. In this paper we answer negatively a question posed in Sloan et al. (2017) concerning an anticipated formula for the hydra number of disconnected graphs. On the positive side, we show that the expression which appears in this formula is an upper bound for the hydra number of these graphs.

This second part of the paper presents and discuss results from the implementation of the MILP model presented in Part I. This comprehensive model is intended for the expansion planning of power distribution systems. The results were obtained using the programming language OPL and the minimization problem was solved using the CPLEX solver. We applied the model to three known systems, with 23, 54 and 69 buses, and also to a system with 276 buses containing real data, to illustrate potential uses and advantages of the proposed formulation. For the sake of validation, a comparison was carried out between the results obtained with the linearized model and the results obtained through a conventional load flow, showing the accuracy and efficiency of the model. Furthermore, the results obtained for the 54-bus system were compared with equivalent results obtained with another MILP model.

In this paper a new approach to the Reliability-based Robust Design Optimization (RBRDO) of angle-ply composite laminate structures is presented. The problem is defined as a bi-objective Robust Design Optimization (RDO) problem, with deterministic and probabilistic constraints . Design optimization is considered as the minimization problem of the weight (optimality) and the determinant of the variance-covariance matrix of the response functionals of the system (robustness). Reliability assessment is executed by the Reliability Index Approach (RIA), as an inner cycle. The key concept of this methodology is the exclusive use of evolutionary algorithms with elitist strategy, allowing for global convergence in the two optimization cycles. The RIA problem was reformulated and a set of new evolutionary operators were developed. A numerical example is presented and the results compared with other RBRDO and RDO formulations. Results show that deterministic and probabilistic structural integrity measures are quite sensitive to uncertainty, for multi-component composite structures.

Recently, the l p -norm regularization minimization problem ( P p λ ) has attracted great attention in compressed sensing. However, the l p -norm ‖x‖ p p in problem ( P p λ ) is nonconvex and non-Lipschitz for all p ∈ ( 0 , 1 ) , and there are not many optimization theories and methods proposed to solve this problem. In fact, it is NP-hard for all p ∈ ( 0 , 1 ) and λ > 0 . In this paper, we study one modified l p -norm regularization minimization problem to approximate the NP-hard problem ( P p λ ) . Inspired by the good performance of Half algorithm in some sparse signal recovery problems, an iterative thresholding algorithm is proposed to solve our modified l p -norm regularization minimization problem ( P p , 1 ∕ 2 , ϵ λ ) . Numerical results on some sparse signal recovery problems show that our algorithm performs effectively in finding the sparse signals compared with some state-of-art methods.

We consider a minimization problem for the variational functional associated with a Gross–Pitaevskii equation arising in the study of an attractive Bose–Einstein condensate. Under an ellipse-shaped trapping potential, that is, the bottom of the trapping potential is an ellipse, we prove that any minimizer of the minimization problem blows up at one of the endpoints of the major axis of the ellipse if the parameter associated to the attractive interaction strength approaches a critical value.

We consider variational integral functionals ∫ Ω g ( x , u ( x ) , D u ( x ) ) d x , where Ω is a bounded open subset in R n and the integrand g ( x , s , ξ ) = f ( x , ξ ) + b ( x ) s is not subjected to any growth condition from above neither satisfies any regularity assumption, growing linearly with respect to the s -variable. Their interest relies on the fact that they are strictly connected with optimal transport problems with congestion effects. The aim of this paper is to find sufficient conditions on the boundary datum u ∗ in order to obtain global and explicit estimates for the solutions of the following minimization problem min ∫ Ω g ( x , u ( x ) , D u ( x ) ) d x ; u ∈ u ∗ + W 0 1 , 1 ( Ω ) .

Arnoldi method approximates exterior eigenvalues of a large sparse matrix, but may fail to approximate corresponding eigenvectors. The refined Arnoldi method approximates an eigenpair by solving a related singular value problem. In this paper, we propose a new procedure to extract an approximate eigenpair from a Krylov subspace in Arnoldi method, using a minimization problem. Unlike the refined Arnoldi method, the suggested procedure requires solving a linear system.

This paper considers the regularization parameter determination of l 1 -regularized minimization problem. We solve the l 1 -regularized problem using iterative reweighted least squares (IRLS) which involves solving a linear system whose coefficient matrix has the form α M + ( 1 − α ) N ( α ∈ ( 0 , 1 ) ). The aim of this paper is to find an efficient and computationally inexpensive algorithm to both choose the regularization parameter and solve the l 1 -regularized problem. In order to achieve this, we propose an IRLS algorithm with adaptive regularization parameter selection based on a heuristic parameter determination rule—de Boor’s parameter selection criterion. Compared with some of the state-of-the-art algorithms and parameter selection rules, the numerical experiments show the efficiency and robustness of the proposed method.

We study the following minimization problem (0.1) e β ( b ) : = inf { u ∈ H 1 ( R 2 ) : ∫ R 2 | u | 2 d x = 1 } ⁡ E β b ( u ) , where E β b ( ⋅ ) is some kind of Kirchhoff functional (the precise form is given by (1.2) below) with a periodic potential. We prove that problem (0.1) can be attained for all β ≥ β ⁎ provided that b > 0 is small enough, which is different from the case of b = 0 . Moreover, we are surprised to discover that the limits of minimizers of (0.1) as b → 0 + for the cases of β = β ⁎ and β > β ⁎ are totally different. Up to rescaling, in the former case the minimizers converge to Q ( x ) in H 1 ( R 2 ) , where Q ( x ) is the unique positive solution of − Δ u + u − u 3 = 0 . However, in the latter case the minimizers converge to a minimizer of (0.1) with b = 1 and potential V ( x ) ≡ 0 .

The multistochastic Monge–Kantorovich problem on the product X = ∏ i = 1 n X i of n spaces is a generalization of the multimarginal Monge–Kantorovich problem. For a given integer number 1 ≤ k n we consider the minimization problem ∫ c d π → inf on the space of measures with fixed projections onto every X i 1 × … × X i k for arbitrary set of k indices { i 1 , … , i k } ⊂ { 1 , … , n } . In this paper we study basic properties of the multistochastic problem, including well-posedness, existence of a dual solution, boundedness and continuity of a dual solution.

In this paper, we establish a non-convex L p norm relaxation model for low Tucker rank tensor recovery problem, and equivalently transform it to a non-convex minimization problem with separable structure by introducing series of auxiliary variables. In particular, we propose two alternating direction method of multipliers (ADMM) based on exact and inexact iteratively reweighted algorithms to solve the obtained non-convex relaxation problem respectively, which are proved to be convergent. We implement the proposed algorithms in numerical experiments for solving low Tucker rank tensor recovery problem on simulation data and real data, and compare them with other existing state-of-art algorithms. Numerical results show the effectiveness of the proposed algorithms for solving low rank tensor recovery problem and image recovery.

This paper discusses the classifier ensemble problem with sparsity and diversity learning, which is a central issue in machine learning. The current approach for reducing the size and increasing the accuracy of a classifier ensemble is to formulate it as a convex quadratic programming problem, which is a relaxation problem, and then solve it by using the existing methods for convex quadratic programming or by computing closed-form solutions. This paper presents a novel computational approach for solving the classifier ensemble problem with sparsity and diversity learning without any recourse to relaxation problems and their associated methods. We first show that the classifier ensemble problem can be expressed as a minimization problem for the sum of certain convex functions over the intersection of fixed point sets of quasi-nonexpansive mappings. Next, we propose fixed point optimization algorithms for solving the minimization problem and show that the algorithms converge to the solution of the minimization problem. It is shown that the proposed algorithms can directly solve the classifier ensemble problem with sparsity and diversity learning. Finally, we compare the performance of the proposed sparsity and diversity learning methods against an existing method in classification experiments using data sets from the UCI machine learning repository and the LIBSVM. The experimental results show that the proposed methods have higher classification accuracies than the existing method.

We propose a novel integration method of binary classifiers for multi-class classification. The proposed method is characterized as a minimization problem of a weighted mixture of Bregman divergence, and employs binary classifiers as class-dependent feature vector. We discuss the statistical properties of the proposed method and the relationship between the proposed method and existing multi-class classification methods, and reveal that many of the existing methods can be formulated as special cases of the proposed method. Small experiments show that the proposed method can effectively incorporate information of multiple binary classifiers into the multi-class classifier.

In this paper we address a one phase minimization problem for a functional that includes the perimeter of the positivity set. It also includes three terms, the first one is ∫ f u and the second ∫ u > 0 h where f and h are bounded functions. The third term is ∫ G ( | ∇ u | ) where G is a smooth convex function. This term generalizes the integral of the | ∇ u | p . As a consequence of our results we find that, when f ≤ 0 , there exists a nonnegative minimizer. Moreover, every nonnegative minimizer is Lipschitz continuous, it is a solution to Δ G u = f in { u > 0 } and satisfies that H = Φ ( | ∇ u | ) − h on the reduced free boundary, ∂ r e d { u > 0 } which, as a consequence, is proved to be as smooth as the data allow. Here Φ ( t ) = t g ( t ) − G ( t ) ( g = G ′ ) and H is the mean curvature of the free boundary.

At many instances, information on the state of a multistate system executing a mission is obtained via the costly inspections performed at discrete instants of time. Therefore, the corresponding cost-wise optimal mission abort policy that takes into account the state of a system should be designed accordingly. In this paper, we introduce an optimal mission abort policy that minimizes the expected costs due to inspections, mission failure and loss of a system. A system operates in a random environment modeled by a renewal process of shocks. With each shock, its state can deteriorate with certain probabilities that can eventually result in the total failure. The decision to abort or to continue operation depends on the number of experienced shocks and on the state of a system that is revealed only at inspections. The corresponding cost minimization problem is formulated and the necessary relationships for solving it are derived. Detailed numerical illustrations and discussions are presented.

In this paper, we first design a time optimal control problem for the heat equation with sampled-data controls, and then use it to approximate a time optimal control problem for the heat equation with distributed controls. The study of such a time optimal sampled-data control problem is not easy, because it may have infinitely many optimal controls. We find connections among this problem, a minimal norm sampled-data control problem and a minimization problem, and obtain some properties on these problems. Based on these, we not only build up error estimates for optimal time and optimal controls between the time optimal sampled-data control problem and the time optimal distributed control problem, in terms of the sampling period, but we also prove that such estimates are optimal in some sense.

In order to reduce weight and to create efficient construction, fiber reinforced plastics are of general interest. Hence, the understanding of the material behavior is very important to build safe structures. For composite structures, existing of several stacked layers, which behave transversely isotropic, different failure mechanisms may appear. The considerations in this paper deal with the failure analysis of one layer of a laminated structure with unidirectionally orientated fibers. The possible failure mechanisms are described with failure criteria. So-called damage models include these criteria and the behavior of damaged structures, formulated in degradation models. Damage models usually show a strong mesh dependency in their inelastic part, which begins with an initial failure in the structure and ends with the total loss of stiffness. This mesh dependency is characterized by the concentration of the occurring damage only within a small zone, which generally corresponds e.g. with one element row and thus with the mesh refinement. In order to develop a regularized damage model for transversely isotropic materials a gradient enhancement based on the Helmholtz free energy function is used. With the introduction of a new field, coupled with the inelastic variables, the model gets a non-local character, preserving C 0 -interpolation order. Formulated as a pure minimization problem, the elimination of the mesh dependency due to the unambiguity of the solution is illustrated by numerical examples.

The profile minimization problem is a graph layout problem that consists of finding a linear arrangement (labeling) of vertices of a graph such that the sum of profiles of all vertices is minimum. The profile of a vertex can be defined as the difference of the position of its left most neighbor and the position of that vertex in the linear arrangement. It is an NP-complete problem with applications in the areas where the reordering of rows and columns of a sparse matrix is required in order to reduce the storage space. In this work, we propose a hybrid simulated annealing algorithm with the aim of profile reduction of a given graph by incorporating spectral sequencing for generating the initial solution. Experiments conducted on some benchmark graphs show that our algorithm outperforms the best existing algorithm in some cases and is comparable for rest of the instances. It also attains the optimal values for some classes of graphs with known optimal results.

Poles assignment problem for second-order linear periodic system by using periodic proportion-plus-derivative (PD) state-feedback is considered in this paper. The poles assignment problem via periodic PD state-feedback in a class of discrete periodic second-order linear systems can be transformed into the problem of solving a class of constrained discrete periodic regulator equations. A complete parametric approach to poles assignment via periodic PD state-feedback is proposed based on the solutions to the discrete periodic regulator matrix equations. Based on the proposed parametric method, the consideration of the minimization problem and the robust problem of the plant system are proposed. Two numerical examples are presented to illustrate the effectiveness of the proposed approaches.

The aim of super-resolution (SR) algorithms is to recover high-resolution (HR) images and videos from low-resolution (LR) ones. Since the SR is considered as an ill-posed minimization problem, regularization techniques are then considered. The choice of the regularization term plays a major role in the quality of the obtained HR image. Even if many terms have been proposed in the literature, they still suffer from different undesirable artifacts. To address these weaknesses, we propose a variational SR model based on Huber-Norm using Bregman distances. This offers the new model to be more consistent against contrast loss and smoothing gray values, in contrast, strong edges and contours are well preserved in the reconstruct HR image. Moreover, the use of first-order primaldual algorithm with an adaptive regularization parameter choice assure the convergence to the desired HR image, in a fast way, preserving important image features. As a result, the proposed algorithm shows promising results for various real and synthetic datasets compared with other methods. We treat the multi-frame super-resolution task based on Bregman distance.We propose a variational SR model based on Huber-Norm and bilateral total variation.The improved regularization is efficient in degraded image super-resolution task using primaldual algorithm.The proposed method gives better performance comparing with other approaches.

We study the following minimization problem (P) m p ( ρ ) = inf ⁡ { E p ( u ) : u ∈ S ρ } , where E p ( u ) is the Schrodinger–Poisson–Slater functional with unbounded potential E p ( u ) = 1 2 ∫ R 3 ( | ∇ u | 2 + V ( x ) | u | 2 ) d x + 1 4 ∫ R 3 ∫ R 3 | u ( x ) | 2 | u ( y ) | 2 | x − y | d x d y − 1 p + 2 ∫ R 3 | u | p + 2 d x , and the constraint S ρ is given by S ρ = { u : ∫ R 3 | u | 2 d x = ρ and ∫ R 3 | ∇ u | 2 + V ( x ) | u | 2 d x ∞ } . We prove that, when 0 p p ⁎ : = 4 / 3 , (P) admits one minimizer for any ρ > 0 ; when p = p ⁎ , (P) is attained if and only if ρ ≤ ρ p ⁎ with ρ p ⁎ > 0 given by (1.11) . Moreover, for each fixed ρ > ρ p ⁎ , we show the concentration behavior of minimizers as the exponent p tends from below to the critical exponent p ⁎ .

The present paper shows an extension of the theory of principal partitions for submodular functions to that for bisubmodular functions. We examine the structure of the collection of all solutions of a parametric minimization problem described by a bisubmodular function and two vectors. The bisubmodular function to be minimized for each parameter is the sum of the bisubmodular function and a parameterized box-bisubmodular function given in terms of the two vectors. We show that the collection of all the minimizers for all parameters forms a signed ring family and it thus induces a signed poset on a signed partition of the underlying set. We further examine the structure of the signed ring family and reveal the decomposition structure depending on critical values of the parameter. Moreover, we discuss the relation between the results of this paper on bisubmodular functions and the theory of principal partitions developed for submodular functions.

In this work, the synthesis of a full order dynamic output feedback controller (DOFC) for Fractional-Order Systems with a derivative order 1 H ∞ control. The existence conditions and design of DFOS are given. An LMI-based minimization problem is derived based on the H ∞ -norm computation for fractional order systems. Finally, simulation results are presented to illustrate the performance of the proposed methodology.

High reconstructed performance compressed video sensing (CVS) with low computational complexity and memory requirement is very challenging. In order to reconstruct the high quality video frames with low computational complexity, this paper proposes a tensor-based joint sparseness regularization CVS reconstruction model FrTVCST (fractional-order total variation combined with sparsifying transform), in which a high-order tensor fractional-order total variation (FrTV) regularization and a tensor discrete wavelet transform (DWT) L0 norm regularization are combined. Furthermore, an approach for choosing the regularization parameter that controls the influence of the two terms in this joint model is proposed. Afterwards, a tensor gradient projection algorithm extended from smoothed L0 (SL0) is deduced to solve this combined tensor FrTV and DWT joint regularization constrained minimization problem, using a smooth approximation of the L0 norm. Compared with several state-of-the-art CVS reconstruction algorithms, such as the Kronecker compressive sensing (KCS), generalized tensor compressive sensing (GTCS), N-way block orthogonal matching pursuit (N-BOMP), low-rank tensor compressive sensing (LRTCS), extensive experiments with commonly used video data sets show the competitive performance of the proposed algorithm with respect to the peak signal-to-noise ratio (PSNR) and subjective visual quality. A FrTV combined with tensor DWT for CS video reconstruction model is proposed.A method for estimating the regularization parameter is proposed.A tensor smoothed L0 algorithm is developed to solve this reconstruction model.The algorithm has a higher PSNR and better detail preservation.

This paper focuses on the management of red blood cells (RBCs) by a large medical center within a regional blood exchange network. We provide both a theoretical and managerial contribution to the periodic-review fixed lifetime perishable inventory literature by considering multiple independent sources of supply. One source supplies blood via a typical standing order process. The other sources are smaller lower usage hospitals that randomly transfer blood to the medical center. Transferred blood is characterized by a much shorter average lifetime than blood supplied via standing order and introduces additional uncertainty into the inventory management process. We propose a solution approach that can be readily applied in practice and solve the multi-period cost minimization problem using a dynamic program. We provide numerical examples and demonstrate that our solution approach outperforms a corresponding base stock policy as well as the ordering policy that was actually used by the medical center.

As a special 2D rectangle packing problem, the 2D rectangle packing area minimization problem with central rectangle (CR-RPAMP) has one or more central rectangles among the candidate items. The central rectangles should be packed near the center of the final layout. At the same time, the length–width ratio of the final layout must be within a reasonable region. The CR-RPAMP has been applied in many areas such as the layout design of semi-submersible platform, farmland irrigation, urban planning. In this study, to improve the performance of heuristic approach for solving the CR-RPAMP, three novel strategies including strategy of filling inner space, strategy of generating inner space and strategy of simplifying packing process, are proposed and combined to form a novel heuristic approach NHACR (Novel Heuristic Approach for CR-RPAMP). The analyses of computational complexity of the proposed NHACR indicate that it has low computational complexity. Based on two famous sets of benchmark instances, the proposed NHACR shows better performance compared with several existing algorithms considering the success rate, the filling rate of final layout and the computing time. Finally, the NHACR is utilized to solve a specific application problem in oil and gas industry and its advantage is further confirmed.

In this paper, we study the existence of critical points for the following functional I ( u ) = 1 2 ∫ R N | ∇ u | 2 + ∫ R N | u | 2 | ∇ u | 2 − N 4 ( N + 1 ) ∫ R N | u | 4 ( N + 1 ) N , constrained on S c = { u ∈ H 1 ( R N ) | ∫ R N | u | 2 | ∇ u | 2 + ∞ , | u | 2 = c , c > 0 } , where N ≥ 1 . The constraint problem is L 2 -critical. We prove that the minimization problem i c = inf u ∈ S c ⁡ I ( u ) has no minimizer for all c > 0 . We also obtain a threshold value of c separating the existence and nonexistence of critical points for I ( u ) restricted to S c .

We model the Haplotype Assembly Problem (HAP) as a minimization problem over an ( n − 1 ) -dimensional sphere, where n is the haplotype length. A manifold optimization approach is proposed to solve this problem. To escape the saddle points, the Riemannian trust region method is utilized and its convergence is proved. Simulation results over both real and synthetic data show that the proposed method is considerably accurate for haplotype estimation.

In this paper, a direction of arrival (DOA) estimation algorithm for coherent distributed (CD) sources considering unknown mutual coupling in massive MIMO systems is proposed. By utilizing an enhanced sample covariance matrix (SCM) that matches well with massive MIMO systems, the proposed algorithm constructs a perturbed model and further exploits the sparse total east squares (STLS) technique to achieve DOA and angular spread estimation. With the DOA and angular spread estimates, the mutual coupling coefficients are given by solving the constrained minimization problem. Compared with the other state-of-the-art algorithms, the proposed algorithm not only can provide improved DOA estimation performance, but also can conquer the deficient scenario in a much easier way. Theoretical performance analysis and numerical examples validate the effectiveness of the proposed algorithm.

We investigate the existence, the non-existence and the asymptotic behavior of the least-energy solutions of a semilinear elliptic equation with the Hardy–Sobolev critical exponent. In the boundary singularity case, it is known that the mean curvature of the boundary at origin plays a crucial role on the existence of the least-energy solutions. In this paper, we study the relation between the asymptotic behavior of the solutions and the mean curvature at origin.

Image deconvolution is an ill-posed problem that requires a regularization term to solve. The most common forms of image priors used as the regularization term in image deconvolution tend to produce smoothed (slightly blurry) images, hence don’t well reconstruct image details. In this paper, a new image prior is introduced. This prior is used as a regularization term to model the non-blind image deconvolution problem. The complete regularization term consists of two parts: one that penalizes non-sparsity of the gradient, and the other that penalizes the blurriness in the image. The resulting regularization term favors sharp images over blurry ones. It means that the minimum of this term corresponds to the true sharp solution. The minimization problem is non-convex and we propose a scheme based on half-quadratic regularization. We demonstrate the efficiency of the proposed method by performing several quantitative and qualitative comparisons with the existing non-blind image deconvolution methods for deblurring artificial and real blurred images. The experimental results show that the proposed method tends to well reconstruct image details whilst suppresses noise. In addition, the reconstructed images have a higher PSNR and a lower blurriness value compared to those in the existing methods.

The outage probability (OP) performance of mobile device-to-device (D2D) cooperative networks with incremental amplify-and-forward (IAF) relaying and transmit antenna selection (TAS) is investigated in this paper. The exact closed-form OP expressions are derived for two TAS schemes. Based on the derived closed-form OP expressions, a power allocation minimization problem is formulated. Then through Monte Carlo simulations under different conditions, we have verified the accuracy of the derived OP expressions. The simulation results showed that the power allocation parameter has an important influence on the OP performance.

The maximal sum of a sequence "A" of "n" real numbers is the greatest sum of all elements of any strictly contiguous and possibly empty subsequence of "A", and it can be computed in "O(n)" time by means of Kadane's algorithm. Letting "A^(x -> p)" denote the sequence which results from inserting a real number "x" between elements "A[p-1]" and "A[p]", we show how the maximal sum of "A^(x -> p)" can be computed in "O(1)" worst-case time for any given "x" and "p", provided that an "O(n)" time preprocessing step has already been executed on "A". In particular, this implies that, given "m" pairs "(x_0, p_0), ..., (x_{m-1}, p_{m-1})", we can compute the maximal sums of sequences "A^(x_0 -> p_0), ..., A^(x_{m-1} -> p_{m-1})" in "O(n+m)" time, which matches the lower bound imposed by the problem input size, and also improves on the straightforward strategy of applying Kadane's algorithm to each sequence "A^(x_i -> p_i)", which takes a total of "Theta(n.m)" time. Our main contribution, however, is to obtain the same time bound for the more complicated problem of computing the greatest sum of all elements of any strictly or circularly contiguous and possibly empty subsequence of "A^(x -> p)". Our algorithms are easy to implement in practice, and they were motivated by and find application in a buffer minimization problem on wireless mesh networks., 13 pages, 4 figures, 2 tables. Accepted for journal publication

We consider the maximum flow time minimization problem in batch scheduling, which is a capacitated version of broadcast scheduling. In this setting, n different pages of information are available at the server which receives requests from clients over time for specific pages. The server can transmit at most one page p at each time to satisfy a batch of requests for the same page p , up to a certain capacity B p . In this paper we give the first ( 1 + ϵ ) -approximations for this problem with arbitrarily small resource augmentation, using either more capacity or more speed.

We develop a moment-equation-copula-closure method for the inexpensive approximation of the steady state statistical structure of strongly nonlinear systems which are subjected to correlated excitations. Our approach relies on the derivation of moment equations that describe the dynamics governing the two-time statistics. These are combined with a non-Gaussian pdf representation for the joint response-excitation statistics, based on copula functions that has (i) single time statistical structure consistent with the analytical solutions of the Fokker–Planck equation, and (ii) two-time statistical structure with Gaussian characteristics. Through the adopted pdf representation, we derive a closure scheme which we formulate in terms of a consistency condition involving the second order statistics of the response, the closure constraint. A similar condition, the dynamics constraint, is also derived directly through the moment equations. These two constraints are formulated as a low-dimensional minimization problem with respect to the unknown parameters of the representation, the minimization of which imposes an interplay between the dynamics and the adopted closure. The new method allows for the semi-analytical representation of the two-time, non-Gaussian structure of the solution as well as the joint statistical structure of the response-excitation over different time instants. We demonstrate its effectiveness through the application on bistable nonlinear single-degree-of-freedom energy harvesters with mechanical and electromagnetic damping, and we show that the results compare favorably with direct Monte-Carlo simulations., Samsung Scholarship Foundation, MIT Energy Initiative

In this paper we will find optimal lower bound for the first eigenvalue of the fourth order equation with integrable potentials when the L 1 norm of potentials is known. We establish the minimization characterization for the first eigenvalue of the measure differential equation, which plays an important role in the extremal problem of ordinary differential equation. The conclusion of this paper will illustrate a new and very interesting phenomenon that the minimizing measures will no longer be located at the center of the interval when the norm is large enough.

Electric energy storage is one of the most promising and convenient solutions for energy cost management of buildings by shifting electric loads. This paper investigates electric energy storage (EES) size planning to minimize the total electricity cost of buildings, including investment. This study discusses EES planning considering an EES operation, especially focusing on an economically optimized decision of EES capacity. We first formulate a general electricity cost minimization problem with the electricity bill of buildings and EES cost, and decompose the problem into two parts for EES planning and EES operations. The EES planning algorithm based on the iteration process is proposed considering an ESS operation. The simulation demonstrates that the proposed EES planning can perform close to the optimal exhaustive search algorithm.

Connected Vehicles (CV) equipped with a Speed Advisory System (SAS) can obtain and utilize upcoming traffic signal information to manage their speed in advance, lower fuel consumption, and improve ride comfort by reducing idling at red lights. In this paper, a SAS for pre-timed traffic signals is proposed and the fuel minimal driving strategy is obtained as an analytical solution to a fuel consumption minimization problem. We show that the minimal fuel driving strategy may go against intuition of some people; in that it alternates between periods of maximum acceleration, engine shut down, and sometimes constant speed, known in optimal control as bang-singular-bang control. After presenting this analytical solution to the fuel minimization problem, we employ a sub-optimal solution such that drivability is not sacrificed and show fuel economy still improves significantly. Moreover this paper evaluates the influence of vehicles with SAS on the entire arterial traffic in micro-simulations. The results show that SAS-equipped vehicles not only improve their own fuel economy, but also benefit other conventional vehicles and the fleet fuel consumption decreases with the increment of percentage of SAS-equipped vehicles. We show that this improvement in fuel economy is achieved with a little compromise in average traffic flow and travel time.

This work proposes a new optimization method called root tree optimization algorithm (RTO). The robustness and efficiency of the proposed RTO algorithm is validated on a 23 standard benchmark nonlinear functions and compared with well-known methods by addressing the same problem. Simulation results show effectiveness of the proposed RTO algorithm in term of solution quality and convergence characteristics. In order to evaluate the effectiveness of the proposed method, 3-unit, 30 Bus IEEE, 13-unit and 15-units are used as case studies with incremental fuel cost functions. The constraints include ramp rate limits, prohibited operating zones and the valve point effect. These constraints make the economic dispatch (ED) problem a non-convex minimization problem with constraints. Simulation results obtained by the proposed algorithm are compared with the results obtained using other methods available in the literature. Based on the numerical results, the proposed RTO algorithm is able to provide better solutions than other reported techniques in terms of fuel cost and robustness.

In recent years, several works proposed local search heuristics for round robin sport scheduling problems. It is known that the neighborhood structures used in those works do not fully connect the solution space. The aim of this paper is to present a novel neighborhood structure for single round robin sport scheduling problems. The neighborhood structure is described in graph theory terms and its correctness is proven. We show that the new neighborhood structure increases the connectivity of the solution space when compared to previous neighborhood structures. We evaluate its performance using the Traveling Tournament Problem with Predefined Venues and the Weighted Carry-Over Effects Value Minimization Problem as case studies. HighlightsSeveral works proposed local search heuristics for round robin sport scheduling problems.The neighborhood structures used in those works do not connect the solution space.We present a novel neighborhood structure for single round robin sport scheduling problems.The neighborhood structure is described in graph theory terms and its correctness is proven.The new neighborhood structure increases the connectivity of the solution space.