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Neighbourhood search algorithms are often the most effective known approaches for solving partitioning problems. In this paper, we consider the capacitated examination timetabling problem as a partitioning problem and present an examination timetabling methodology that is based upon the large neighbourhood search algorithm that was originally developed by Ahuja and Orlin. It is based on searching a very large neighbourhood of solutions using graph theoretical algorithms implemented on a so-called improvement graph. In this paper, we present a tabu-based large neighbourhood search, in which the improvement moves are kept in a tabu list for a certain number of iterations. We have drawn upon Ahuja-Orlin's methodology incorporated with tabu lists and have developed an effective examination timetabling solution scheme which we evaluated on capacitated problem benchmark data sets from the literature. The capacitated problem includes the consideration of room capacities and, as such, represents an issue that is of particular importance in real-world situations. We compare our approach against other methodologies that have appeared in the literature over recent years. Our computational experiments indicate that the approach we describe produces the best known results on a number of these benchmark problems. [ABSTRACT FROM AUTHOR]

In this paper, we present a feasible predictor-corrector interior-point method for symmetric cone optimization problem in the large neighbourhood of the central path. The method is generalization of Ai-Zhang's predictor-corrector algorithm to the symmetric cone optimization problem. Starting with a feasible point in given large neighbourhood of the central path, the algorithm still terminates in at most iterations. This matches the best known iteration bound that is usually achieved by short-step methods, thereby, closing the complexity gap between long- and short-step interior-point methods for symmetric cone optimization. The preliminary numerical results on a selected set of NETLIB problems show advantage of the method in comparison with the version of the algorithm that is not based on the predictor-corrector scheme. [ABSTRACT FROM AUTHOR]

Concave knapsack problems with integer variables have many applications in real life, and they are NP-hard. In this paper, an exact and efficient algorithm is presented for concave knapsack problems. The algorithm combines the contour cut with a special cut to improve the lower bound and reduce the duality gap gradually in the iterative process. The lower bound of the problem is obtained by solving a linear underestimation problem. A special cut is performed by exploiting the structures of the objective function and the feasible region of the primal problem. The optimal solution can be found in a finite number of iterations, and numerical experiments are also reported for two different types of concave objective functions. The computational results show the algorithm is efficient. [ABSTRACT FROM AUTHOR]

This paper develops a parameter estimation algorithm for linear continuous-time systems based on the hierarchical principle and the parameter decomposition strategy. Although the linear continuous-time system is a linear system, its output response is a highly nonlinear function with respect to the system parameters. In order to propose a direct estimation algorithm, a criterion function is constructed between the response output and the observation output by means of the discrete sampled data. Then a scheme by combining the Newton iteration and the least squares iteration is builded to minimise the criterion function and derive the parameter estimation algorithm. In light of the different features between the system parameters and the output function, two sub-algorithms are derived by using the parameter decomposition. In order to remove the associate terms between the two sub-algorithms, a Newton and least squares iterative algorithm is deduced to identify system parameters. Compared with the Newton iterative estimation algorithm without the parameter decomposition, the complexity of the hierarchical Newton and least squares iterative estimation algorithm is reduced because the dimension of the Hessian matrix is lessened after the parameter decomposition. The experimental results show that the proposed algorithm has good performance. [ABSTRACT FROM AUTHOR]

This paper presents a Quality of Service (QoS) guaranteed dynamic grid resource scheduling algorithm. It mainly deals with multiple QoS-based grid resource scheduling models and solves the scheduling problems using optimization techniques. The paper proposes the idea of decomposing a global optimization problem in multiple QoS-based resource scheduling into two sub-problems, which simplifies the problem and makes it mathematically tractable. An iterative algorithm is also presented to get grid users and grid resource providers to interact with each other in an interactive process in resource market and achieve optimal QoS constraint dynamic grid resource scheduling. The paper provides performance studies comparing the proposed optimal approach with three possible easier approaches, which provide only partial optimization. The experimental results show that the proposed approach considering both computation and network traffic is able to better optimize the execution time than approaches, which consider only one or none of these criteria. [ABSTRACT FROM AUTHOR]

In order to realize accurate control of underwater vehicles, this paper proposed a fractal prediction model of surge. Firstly, we introduce the current state-of-the-art of fractal prediction; secondly, we complete a fractal analysis with the R_S method, calculating the fractal dimension of surge using the short-time dimension method; thirdly, we correct the vertical scaling factor of the Iterated Function System (IFS) using the fractal dimension. Then the predictive value can be calculated through anti-iteration according to the statistical significantly IFS and proposing a fractal prediction model. Finally, we complete a simulation analysis based on the actual data and a comparison to another prediction algorithm. The result shows that the fractal prediction algorithm of this article has better comprehensive performance. [ABSTRACT FROM PUBLISHER]

In this paper, iterative algorithm for strong vector equilibrium problem (SVEP) is studied. Firstly, an auxiliary problem for SVEP is introduced and the relationships between these two problems are discussed. Then, based on the auxiliary problem, a projection iterative algorithm for SVEP is proposed. Moreover, analysis of convergence of this iterative algorithm is investigated under suitable conditions of continuity and convexity. The main result obtained in this paper generalizes and improves the corresponding ones of Iusem and Sosa [Iusem AN, Sosa W. Iterative algorithms for equilibrium problems. Optimization. 2003;52(3):301–316.] and Cheng and Liu [Cheng B, Liu SY. An iterative algorithm for vector equilibrium problems. J. Lanzhou Univ. (Nat. Sci.). 2009;45(5):105–109.]. [ABSTRACT FROM AUTHOR]

The Cauchy problem for the Helmholtz equation is considered. It was demonstrated in a previous paper by the authors that the alternating algorithm suggested by V.A. Kozlov and V.G. Maz’ya does not converge for large wavenumbers k in the Helmholtz equation. Here, we present some simple modifications of the algorithm which may restore the convergence. They consist of the replacement of the Neumann-Dirichlet iterations by the Robin-Dirichlet ones which repairs the convergence for less than the first Dirichlet-Laplacian eigenvalue. In order to treat large wavenumbers, we present an algorithm based on iterative solution of Robin-Dirichlet boundary value problems in a sufficiently narrow border strip. Numerical implementations obtained using the finite difference method are presented. The numerical results illustrate that the algorithms suggested in this paper, produce convergent iterative sequences. [ABSTRACT FROM AUTHOR]

Recently, Salkuyeh and Fahim [A new iterative refinement of the solution of ill-conditioned linear system of equations, Int. Comput. Math. 88(5) (2011), pp. 950–956] have proposed a two-step iterative refinement of the solution of an ill-conditioned linear system of equations. In this paper, we first present a generalized two-step iterative refinement procedure to solve ill-conditioned linear system of equations and study its convergence properties. Afterward, it is shown that the idea of an orthogonal projection technique together with a basic stationary iterative method can be utilized to construct a new efficient and neat hybrid algorithm for solving the mentioned problem. The convergence of the offered hybrid approach is also established. Numerical examples are examined to demonstrate the feasibility of proposed algorithms and their superiority to some of existing approaches for solving ill-conditioned linear system of equations. [ABSTRACT FROM PUBLISHER]

This paper presents a method for determining the optimum number, impedance, and locations of fault current limiter (FCL) to reduce the negative impact of distributed generations presence in the power systems such as increasing the short circuit current levels and improve the system reliability. In the considered method, we have modeled the FCL placement as an optimization problem while the objectives are; bus fault current difference, reliability, the number and impedance of FCLs. Moreover, to solve the proposed problem, a new multi-objective optimization algorithm based on firework algorithm namely multi-objective firework algorithm has been implemented. In the new algorithm, several iterations have been considered, and the non-dominated solutions are extracted and stored in an external repository in the iterations. Finally, a fuzzy clustering technique is used to control the size of the repository during the algorithm evolution. The proposed approach is tested on two different systems, namely, Roy Billinton Test System (RBTS) 2 and RBTS 4 test system. The obtained results demonstrate the effectiveness and feasibility of the new method. [ABSTRACT FROM PUBLISHER]

In this paper,we propose a new predictor–corrector interior-point method for symmetric cone programming. This algorithm is based on a wide neighbourhood and the Nesterov–Todd direction. We prove that, besides the predictor steps, each corrector step also reduces the duality gap by a rate of, whereris the rank of the associated Euclidean Jordan algebras. In particular, the complexity bound is, whereis a given tolerance. To our knowledge, this is the best complexity result obtained so far for interior-point methods with a wide neighbourhood over symmetric cones. The numerical results show that the proposed algorithm is effective. [ABSTRACT FROM AUTHOR]

Sparsity of a classifier is a desirable condition for high-dimensional data and large sample sizes. This paper investigates the two complementary notions of sparsity for binary classification: sparsity in the number of features and sparsity in the number of examples. Several different losses and regularizers are considered: the hinge loss and ramp loss, and ℓ2, ℓ1, approximate ℓ0, and capped ℓ1regularization. We propose three new objective functions that further promote sparsity, the capped ℓ1regularization with hinge loss, and the ramp loss versions of approximate ℓ0and capped ℓ1regularization. We derive difference of convex functions algorithms (DCA) for solving these novel non-convex objective functions. The proposed algorithms are shown to converge in a finite number of iterations to a local minimum. Using simulated data and several data sets from the University of California Irvine (UCI) machine learning repository, we empirically investigate the fraction of features and examples required by the different classifiers. [ABSTRACT FROM PUBLISHER]

In this paper, the nonlinear iterative methods, which are different from the classical algorithms, to solve inverse problems are presented. Our methods by denoting some parameters and some properties of the algorithm in both noise and noiseless cases are studied. Finally, the convergence of the sequence generated by the algorithm without noise is discussed. [ABSTRACT FROM AUTHOR]

The consensus reaching process is a dynamic and iterative process for improving group's consensus level before making a final decision in group decision-making (GDM). As the experts will express their opinions under their own intellectual level from different aspects, it is natural that the experts’ weights should reflect their judgment information. This paper proposes a dynamic way to adjust weights of decision-makers (DMs) automatically when they are asked to give original judgment information for GDM problems, in which the DMs express their judgment information by hesitant fuzzy preference relations (HFPRs). Two indices, an individual consensus index of hesitant fuzzy preference relation (ICIHFPR) and a group consensus index of hesitant fuzzy preference relation (GCIHFPR), are introduced. Normalisation of HFPRs with different numbers of possible values is taken into consideration for better computation and comparison. An iterative consensus reaching algorithm is presented with DMs’ weighting vector changing in each consensus reaching process and the process terminates until both theICIHFPRandGCIHFPRare controlled within predefined thresholds. Finally, an example is illustrated and comparative analyses demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a predictor-corrector infeasible-interior-point method for symmetric cone linear complementarity problem (SCLCP) with the Cartesian-property (-SCLCP). This method is based on a wide neighbourhood, which is an even wider neighbourhood than the negative infinity neighbourhood. We show that the iteration-complexity bound of the proposed algorithm for a commutative class of search directions is, whereis the condition number of matrixG,is the handicap of the problem,ris the rank of the associated Euclidean Jordan algebra andis a given tolerance. To our knowledge, this is the best complexity result obtained so far for the wide neighbourhood infeasible-interior-point methods for the Cartesian-SCLCPs. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the problem of stability analysis for linear delta operator systems subject to state saturation. Both full state saturation and partial state saturation are investigated for the delta operator systems. Two equivalent necessary and sufficient conditions are identified such that the system with full state saturation is globally asymptotically stable. Based on the sufficient conditions, an iterative algorithm is proposed for testing global asymptotic stability of the system with full state saturation. A new globally asymptotically stable condition is also proposed for the partial state saturation system. Two numerical examples on a ball and beam model are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of weak sharpness for set-valued variational inequalities in then-dimensional Euclidean space and then present some characterizations of weak sharpness. We also give some examples to illustrate this notion. Under the assumption of weak sharpness, by using the inner limit of a set sequence we establish a sufficient and necessary condition to guarantee the finite termination of an arbitrary algorithm for solving a set-valued variational inequality involving maximal monotone mappings. As an application, we show that the sequence generated by the hybrid projection-proximal point algorithm proposed by Solodov and Svaiter terminates at solutions in a finite number of iterations. These obtained results extend some known results of classical variational inequalities. [ABSTRACT FROM PUBLISHER]

Parallel machine scheduling problems are commonly encountered in a wide variety of manufacturing environments and have been extensively studied. This paper addresses a makespan minimisation scheduling problem on identical parallel machines, in which the specific processing time of each job is uncertain, and its probability distribution is unknown because of limited information. In this case, the deterministic or stochastic scheduling model may be unsuitable. We propose a robust (min–max regret) scheduling model for identifying a robust schedule with minimal maximal deviation from the corresponding optimal schedule across all possible job-processing times (called scenarios). These scenarios are specified as closed intervals. To solve the robust scheduling problem, which is NP-hard, we first prove that a regret-maximising scenario for any schedule belongs to a finite set of extreme point scenarios. We then derive two exact algorithms to optimise this problem using a general iterative relaxation procedure. Moreover, a good initial solution (optimal schedule under a mid-point scenario) for the aforementioned algorithms is discussed. Several heuristics are developed to solve large-scale problems. Finally, computational experiments are conducted to evaluate the performance of the proposed methods. [ABSTRACT FROM PUBLISHER]

For any real matrix A, this paper is concerned with the estimation of the spectral radius of A. The relationship between the weighted norm and the discrete Lyapunov equation of the matrix A is obtained. On the basis of the relationship, an iterative algorithm is presented to obtain the spectral radius of A and to estimate the solution of the corresponding linear discrete system. Several numerical examples are given to show that the iterative algorithm is effective. [ABSTRACT FROM AUTHOR]

In this paper we present some techniques for constructing high-order iterative methods in order to approximate the zeros of a non-linear equation f(x)=0, starting from a well-known family of cubic iterative processes. The first technique is based on an additional functional evaluation that allows us to increase the order of convergence from three to five. With the second technique, we make some changes aimed at minimizing the calculus of inverses. Finally, looking for a better efficiency, we eliminate terms that contribute to the error equation from sixth order onwards. The paper contains a comparative study of the asymptotic error constants of the methods and some theoretical and numerical examples that illustrate the given results. We also analyse the efficiency of the aforementioned methods, by showing some numerical examples with a set of test functions and by using adaptive multi-precision arithmetic in the computation. [ABSTRACT FROM AUTHOR]

This paper describes a cubically convergent iteration method for finding the multiple roots of nonlinear equations, f(x)=0, where f:→ is a continuous function. This work is the extension of our earlier work [P.K. Parida, and D.K. Gupta, An improved regula-falsi method for enclosing simple zeros of nonlinear equations, Appl. Math. Comput. 177 (2006), pp. 769-776] where we have developed a cubically convergent improved regula-falsi method for finding simple roots of f(x)=0. First, by using some suitable transformation, the given function f(x) with multiple roots is transformed to F(x) with simple roots. Then, starting with an initial point x0 near the simple root x* of F(x)=0, the sequence of iterates {xn}, n=0, 1, ... and the sequence of intervals {[an, bn]}, with x*∈{[an, bn]} for all n are generated such that the sequences {(xn-x*)} and {(bn-an)} converges cubically to 0 simultaneously. The convergence theorems are established for the described method. The method is tested on a number of numerical examples and the results obtained are compared with those obtained by King [R.F. King, A secant method for multiple roots, BIT 17 (1977), pp. 321-328.]. [ABSTRACT FROM AUTHOR]

The extended version with the analysis of dynamic system for Wilkinson's iteration improvement of solution is presented in this paper. It turns out that the iteration improvement can be viewed as applying explicit Euler method with step size h=1 to a dynamic system which has a unique globally asymptotically stable equilibrium point, that is, the solution x*=A-1b of linear system Ax=b with non-singular matrix A. As a result, an extended iterative improvement process for solving ill-conditioned linear system of algebraic equations with non-singular coefficients matrix is proposed by following the solution curve of a linear system of ordinary differential equations. We prove the unconditional convergence and derive the roundoff results for the extended iterative refinement process. Several numerical experiments are given to show the effectiveness and competition of the extended iteration refinement in comparison with Wilkinson's. [ABSTRACT FROM AUTHOR]

This paper deals with generalized pattern search (GPS) algorithms for linearly constrained optimization. At each iteration, the GPS algorithm generates a set of directions that conforms to the geometry of any nearby linear constraints. This set is then used to construct trial points to be evaluated during the iteration. In a previous work, Lewis and Torczon developed a scheme for computing the conforming directions, however, the issue of degeneracy merits further investigation. The contribution of this paper is to provide a detailed algorithm for constructing the set of directions whether or not the constraints are degenerate. One difficulty in the degenerate case is the classification of constraints as redundant or nonredundant. We give a short survey of the main definitions and methods for treating redundancy and propose an approach to identify nonredundant ε-active constraints. We also introduce a new approach for handling nonredundant linearly dependent constraints, which maintains GPS convergence properties without significantly increasing computational cost. Some simple numerical tests illustrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we suggest two new iterative methods for finding an element of the solution set of split variational inclusion problem in real Hilbert spaces. Under suitable conditions, we present weak and strong convergence theorems for these methods. We also apply the proposed algorithms to study the split feasibility problem. Finally, we give some numerical results which show that our proposed algorithms are efficient and implementable from the numerical point of view. [ABSTRACT FROM AUTHOR]

H-matrices play an important role in applied sciences such as numerical analysis and optimization theory. An attractive question is to identify whether a given matrix is an H-matrix. In this paper, we propose a new iterative algorithm for identifying H-matrices. We show that the proposed algorithm has linear convergence and can determine the H-matrix characterization for any given matrix. Its performance is illustrated in a set of numerical tests. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm for obtaining the Hermitian positive definite solutions of the nonlinear matrix equation X + A * X -1 A = I is considered and discussed. The convergence of the algorithm is proved. Numerical experiments to illustrate the behavior of the algorithm are executed. [ABSTRACT FROM AUTHOR]

This paper presents an iteration scheme to approximate the producibility of a pattern of holes controlled by a composite position tolerance and produced by an imperfect process. First, the producibility of a two-hole pattern subject to any of three composite position tolerance variants was evaluated by way of numerical integration. The method was then extended to the evaluation of any pattern of n holes (n > 2) by decomposing the pattern and embedding the two-hole numerical approximation algorithm in an iteration scheme. A performance evaluation of the results returned by the numerical approximation against those obtained by simulation was performed and showed very satisfactory performance with a substantial saving in computation time. [ABSTRACT FROM AUTHOR]

The self-updating process (SUP) is a clustering algorithm that stands from the viewpoint of data points and simulates the process how data points move and perform self-clustering. It is an iterative process on the sample space and allows for both time-varying and time-invariant operators. By simulations and comparisons, this paper shows that SUP is particularly competitive in clustering (i) data with noise, (ii) data with a large number of clusters, and (iii) unbalanced data. When noise is present in the data, SUP is able to isolate the noise data points while performing clustering simultaneously. The property of the local updating enables SUP to handle data with a large number of clusters and data of various structures. In this paper, we showed that the blurring mean-shift is a static SUP. Therefore, our discussions on the strengths of SUP also apply to the blurring mean-shift. [ABSTRACT FROM AUTHOR]

In this paper, we propose a non-monotone line search method for solving optimization problems on Stiefel manifold. The main novelty of our approach is that our method uses a search direction based on a linear combination of descent directions and a Barzilai-Borwein line search. The feasibility is guaranteed by projecting each iterate on the Stiefel manifold through SVD (singular value decomposition) factorizations. Some theoretical results for analysing the algorithm are presented. Finally, we provide numerical experiments for comparing our algorithm with other state-of-the-art procedures. The code is available online. The experimental results show that the proposed algorithm is competitive with other approaches and for particular problems, the computational performance is better than the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

The paper describes two fast iterative algorithms for estimating the capacity of automated production lines with finite buffers. These algorithms are based on the linear programming formulation of the problem developed earlier by the author, and provide a range of values in which the throughput of the line is expected to lie. The throughput estimates of the two algorithms, compared with an estimate based on a simple workload analysis, indicate the amount of blocking/starvation as well as the probable causes of this unproductive time. The paper illustrates how inferences can be drawn from the two algorithms and used to improve the loading sequence and lot sizes. Managers can decide if the potential for improvement, which would be to get rid of all blocking/starvation, justifies the time to be spent on such an effort. New alternatives can be developed based on the insights provided by the algorithms and tested quickly. [ABSTRACT FROM AUTHOR]

An original procedure for the determination of the optimum value of tool life criterion of cutting tools tooled with throw-away carbide tips is described in this paper. The procedure has the character of an iterative method, on the basis of which one can reach the optimum value of tool life criterion with respect to attaining the minimum machining cost. The algorithm of the given method is represented in a bar chart, where we can see two calculation cycles, their purpose and other relationships. A practical example closes the paper. [ABSTRACT FROM AUTHOR]

In this paper we extend the stability and stabilizability concepts from the case that the variables are positive real numbers to the case that the variables are positive linear operators. Since the algebra of bounded linear operators is not commutative, such extension does not appear to be obvious. As applications, iterative operator algorithms, converging to some operator means, are discussed. [ABSTRACT FROM PUBLISHER]

In this paper, we report the experimental implementation of handling the reconstruction problem from few angle data-sets for digital holographic microtomography. First, the digital holographic microscopy with sample-rotating scheme is established and few holograms with regularly spaced angle steps are recorded. Then, an algebraic iterative reconstruction algorithm with non-positivity constraint and a smoothing operator is applied to reconstruct three-dimensional refractive index distribution of the measured sample from the few angle data-sets. The experimental results demonstrate that the algebraic iterative technique can accurately reconstruct refractive index distribution from few angle data-sets in digital holographic microtomography. The technique is easy to implement and reduces greatly the required recording times. [ABSTRACT FROM AUTHOR]

Most algorithms for solving linear program require a phase-1 procedure to find a feasible solution. Recently, a dual–primal algorithm for linear optimization has been proposed by Li [Dual–primal algorithm for linear optimization, Optimiz. Methods Softw. 28 (2013), pp. 327–338]. In the process of implementing the dual–primal algorithms, we found an interesting phenomenon that the phase-1 algorithm developed in [Li (2013)] always terminates in one iteration. This fact does not come by chance. A rigorous proof is given in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the Hermitian positive-definite solutions of the matrix equationXs+A*X−tA=Qare considered. New necessary and sufficient conditions for the equation to have a Hermitian positive-definite solution are derived. In particular, whenAis singular, a new estimate of Hermitian positive-definite solutions is obtained. In the end, based on the fixed point theorem, an iterative algorithm for obtaining the positive-definite solutions of the equation withQ=Iis discussed. The error estimations are found. [ABSTRACT FROM AUTHOR]

This paper points out some fatal errors in the equivalent formulations used in Noor 2011 [Noor MA. Projection iterative methods for solving some systems of general nonconvex variational inequalities. Applied Analysis. 2011;90:777–786] and consequently in Noor 2009 [Noor MA. System of nonconvex variational inequalities. Journal of Advanced Research Optimization. 2009;1:1–10], Noor 2010 [Noor MA, Noor KI. New system of general nonconvex variational inequalities. Applied Mathematics E-Notes. 2010;10:76–85] and Wen 2010 [Wen DJ. Projection methods for a generalized system of nonconvex variational inequalities with different nonlinear operators. Nonlinear Analysis. 2010;73:2292–2297]. Since these equivalent formulations are the main tools to suggest iterative algorithms and to establish the convergence results, the algorithms and results in the aforementioned articles are not valid. It is shown by given some examples. To overcome with the problems in these papers, we consider a new system of extended regularized nonconvex variational inequalities, and establish the existence and uniqueness result for a solution of the aforesaid system. We suggest and analyse a new projection iterative algorithm to compute the unique solution of the system of extended regularized nonconvex variational inequalities which is also a fixed point of a nearly uniformly Lipschitzian mapping. Furthermore, the convergence analysis of the proposed iterative algorithm under some suitable conditions is studied. As a consequence, we point out that one can derive the correct version of the algorithms and results presented in the above mentioned papers. [ABSTRACT FROM AUTHOR]

In this paper, we propose an iterative algorithm for a simplified friction problem which is formulated as an elliptic variational inequality of the second kind. We approximate the simplified friction problem by a discrete system with the finite element method. Based on the use of the linearized technique and by constructing a particular function, we put forward the new algorithm to get the discrete solution. This algorithm is attractive due to its simple proof of convergence and easy implementation. A linear equation is solved in each iteration. Numerical results confirm that our algorithm is efficient and mesh independent. [ABSTRACT FROM AUTHOR]

The stochastic approximation problem is to find some roots or minimizers of a nonlinear function whose expression is unknown and whose evaluations are contaminated with noise. In order to accelerate the classical RM algorithm, this paper proposes a new three-term combinatorial direction stochastic approximation algorithm and its general framework which employ a weighted combination of the current noisy gradient and several previous noisy gradients as the iterative direction. Both the almost sure convergence and the asymptotic rate of convergence of the new algorithms are established. Numerical experiments show that the new algorithm outperforms the RM algorithm and another existing combined direction algorithm. [ABSTRACT FROM PUBLISHER]

The hole-free triangular mesh model is a prerequisite for many applications. In this paper, we propose a novel hole-filling algorithm for triangular meshes in engineering which can recover the geometric features of the original meshes. Firstly, the sharp vertices around the hole are extracted and classified into different feature sets. Then the sharp vertex sets are used to construct feature curves with missing parts in the hole by cubic spline interpolation. These feature curves divide the original complex hole into small, flatter sub-holes. Finally, each sub-hole is triangulated into a set of new triangles, and a series of iterative modifications are employed to refine and improve the geometry of hole according to the properties of surrounding mesh. Experimental results demonstrate that the proposed algorithm is powerful enough to recover the missing shape, and the resulted patching meshes interpolate the shape and density of the surrounding mesh and naturally blend with it, which are of good quality for engineering. [ABSTRACT FROM PUBLISHER]

In this paper, we present a novel class of iterative reconstruction methods for severely angular undersampled or/and limited-view tomographic problems with fan-beam scanning geometry. The proposed algorithms are based on a new analytical transform which generalizes Fourier-slice theorem to divergent-beam scanning geometries. Using a non-rigid coordinate transform, divergent rays can be reorganized into parallel ones. Therefore, one can employ a simpler parallel-beam projection model instead of more complicated divergent-beam geometries. Various existing iterative reconstruction techniques for divergent-beam geometries can be easily adapted to the proposed framework. The significant advantage of this formulation is the possibility of exploiting efficient Fourier-based recovery methods without rebinning of the projections. In case of highly sparse measurements (few-view data), rebinning methods are not suitable due to error-prone angular interpolation involved. In this work, three new methods based on the novel analytical framework for fan-beam geometry are presented: the Gerchberg-Papoulis algorithm, the Neumann decomposition method and its total variation regularized version. Presented numerical experiments demonstrate that the methods can be competitive in reconstructing from few-view noisy tomographic measurements. [ABSTRACT FROM AUTHOR]

In this paper, an iterative algorithm for solving the strong vector equilibrium problem with variable domination structure (VSVEP) is considered. First, an auxiliary problem for the VSVEP is introduced and the relationships between the auxiliary problem and VSVEP are discussed. Then, using the auxiliary principle technique, a projection iterative algorithm to compute the approximate solutions of the VSVEP is proposed and analysed. Furthermore, convergence of the iterative sequences generated by this algorithm is investigated under suitable conditions of continuity and convexity. These results extend and improve some recent works in this field. [ABSTRACT FROM AUTHOR]

Recently, Tang et al. [Numer Algorithms. 2014;66(2):379-397] have offered a cyclic iterative method for determining the unique solution of the coupled matrix equations AiXBi = Fi, i = 1, 2,..., N. Analogues to the gradient-based algorithm, the proposed algorithm relies on a fixed parameter whereas it has wider convergence region. Nevertheless, the application of the algorithm to find the centrosymmetric solution of the mentioned problem has been left as a project to be investigated and the optimal value for the fixed parameter has not been derived. In this paper, we focus on a more general class of the coupled linear matrix equations that incorporate the mentioned ones in the earlier refereed work. More precisely, we first develop the authors' propounded algorithm to resolve our considered coupled linear matrix equations over centro-symmetric matrices. Afterwards, we disregard the restriction of the existence of the unique (centro-symmetric) solution and also modify the authors' algorithm by applying an oblique projection technique which allows to produce a sequence of approximate solutions which gratify an optimality property. Numerical results are reported to confirm the validity of the established results and to demonstrate the superior performance of the modified version of the cyclic iterative algorithm. [ABSTRACT FROM AUTHOR]

The coupled-cluster (CC) method is one of the most efficient approaches to describe electron correlation effects in atoms and molecules. The method can be related to other earlier and more conventional methods for an approximate evaluation of the correlation energy like perturbation theory or configuration interaction method. The relations are usually used to suggest possible ways of solving the CC equations. The most popular iterative schemes for obtaining the cluster amplitudes are based on perturbative Jacobi-type procedures but also other algorithms are known from the literature. All of them are characterised by different convergence properties. In the paper, we try to study the efficiency of the basic iterative schemes used in the CC calculations. [ABSTRACT FROM PUBLISHER]

In this paper, we present an iterative algorithm for solving the following coupled Sylvester-transpose matrix equationsover the generalized centro-symmetric matrix group (X1,X2, …,Xq). The solvability of the problem can be determined by the proposed algorithm, automatically. If the coupled Sylvester-transpose matrix equations are consistent over the generalized centro-symmetric matrices, then a generalized centro-symmetric solution group can be obtained within finite iterative steps for any initial generalized centro-symmetric matrix group in the exact arithmetic. Furthermore, it is shown that the least-norm generalized centro-symmetric solution group of the coupled Sylvester-transpose matrix equations can be computed by choosing an appropriate initial iterative matrix group. Moreover, the optimal approximate generalized centro-symmetric solution group to a given arbitrary matrix group (V1,V2, …,Vq) can be derived by finding the least-norm generalized centro-symmetric solution group of a new coupled Sylvester-transpose matrix equations. Finally, some numerical results are given to illustrate the validity and practicability of the theoretical results established in this work. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the properties of a simple locally kernel function. As an application, we present a full-step interior-point algorithm for second-order cone optimization (SOCO). The algorithm uses the simple locally kernel function to determine the search direction and define the neighbourhood of central path. The full step used in the algorithm has local quadratic convergence property according to the proximity function which is constructed by the simple locally kernel function. We derive the iteration complexity for the algorithm and obtain the best-known iteration bound for SOCO. [ABSTRACT FROM AUTHOR]

In this paper, based on a new class of asymptotic l 1 exact penalty functions, we propose a smooth penalty function for solving nonlinear programming problems. One of the main features of our algorithm is that at each iteration, we do not need to solve the global minimum of penalty functions. Furthermore, global convergence property is established without requiring any constraint qualifications. By addressing perturbation functions, we obtain that the lower semi-continuity of the perturbation function at zero is a necessary and sufficient condition to ensure the convergence of the objective function values generated by the algorithm to the optimal value of the primal problem. Since the perturbation function is only dependent on the data of the primal problem, these results enable us to check the convergence property of the algorithm in advance. Finally, we discuss the finite termination of the algorithm when the solution set is non-degenerate or weakly sharp. [ABSTRACT FROM AUTHOR]

Isac and Németh [G. Isac and A. B. Németh, Projection methods, isotone projection cones and the complementarity problem, J. Math. Anal. Appl. 153 (1990), pp. 258–275] proved that solving a coincidence point equation (fixed point problem) in turn solves the corresponding implicit complementarity problem (nonlinear complementarity problem) and they exploited the isotonicity of the metric projection onto isotone projection cones to solve implicit complementarity problems (nonlinear complementarity problems) defined by these cones. In this article an iterative algorithm is studied in connection with an implicit complementarity problem. It is proved that if the sequence generated through the defined algorithm is convergent, then its limit is a solution of the coincidence point equation and thus solves the implicit complementarity problem. Sufficient conditions are given for this sequence to be convergent for implicit complementarity problems defined by isotone projection cones, extending the results of Németh [S.Z. Németh, Iterative methods for nonlinear complementarity problems on isotone projection cones, J. Math. Anal. Appl. 350 (2009), pp. 340–370]. Some existing concepts from the latter paper are extended to solve the problem of finding nonzero solutions of the implicit complementarity problem. [ABSTRACT FROM PUBLISHER]

In this paper, combining the equivalent form of the unified coupled algebraic Riccati equation (UCARE) with the eigenvalue inequalities of a matrix's sum and product, using the properties of an M-matrix and its inverse matrix, we offer new lower and upper matrix bounds for the solution of the UCARE. Furthermore, applying the derived lower and upper matrix bounds and a fixed-point theorem, an existence uniqueness condition of the solution of the UCARE is proposed. Then, we propose a new fixed-point iterative algorithm for the solution of the UCARE. Finally, we present a corresponding numerical example to demonstrate the effectiveness of our results. [ABSTRACT FROM PUBLISHER]

Algebraic reconstruction techniques (ARTs), on both their successive and simultaneous formulations, have been developed since the early 1970s as efficient ‘row-action methods’ for solving the image-reconstruction problem in computerized tomography. In this respect, two important development directions were concerned with, first, their extension to the inconsistent case of the reconstruction problem and, second, their combination with constraining strategies, imposed by the particularities of the reconstructed image. In the first part of this paper, we introduce extending and constraining procedures for a general iterative method of an ART type and we propose a set of sufficient assumptions that ensure the convergence of the corresponding algorithms. As an application of this approach, we prove that Cimmino's simultaneous reflection method satisfies this set of assumptions, and we derive extended and constrained versions for it. Numerical experiments with all these versions are presented on a head phantom widely used in the image reconstruction literature. We also consider hard thresholding constraining used in sparse approximation problems and apply it successfully to a 3D particle image-reconstruction problem. [ABSTRACT FROM PUBLISHER]