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Please wait a minute... For Selected: Download Citations EndNote Ris BibTeX Toggle Thumbnails Select A Mini-Batch Proximal Stochastic Recursive Gradient Algorithm with Diagonal Barzilai–Borwein Stepsize Teng-Teng Yu, Xin-Wei Liu, Yu-Hong Dai, Jie Sun Journal of the Operations Research Society of China    2023, 11 (2): 277-307.   DOI: 10.1007/s40305-022-00436-2 Abstract （1028）      PDF       Knowledge map    Save Many machine learning problems can be formulated as minimizing the sum of a function and a non-smooth regularization term. Proximal stochastic gradient methods are popular for solving such composite optimization problems. We propose a minibatch proximal stochastic recursive gradient algorithm SRG-DBB, which incorporates the diagonal Barzilai–Borwein (DBB) stepsize strategy to capture the local geometry of the problem. The linear convergence and complexity of SRG-DBB are analyzed for strongly convex functions. We further establish the linear convergence of SRGDBB under the non-strong convexity condition. Moreover, it is proved that SRG-DBB converges sublinearly in the convex case. Numerical experiments on standard data sets indicate that the performance of SRG-DBB is better than or comparable to the proximal stochastic recursive gradient algorithm with best-tuned scalar stepsizes or BB stepsizes. Furthermore, SRG-DBB is superior to some advanced mini-batch proximal stochastic gradient methods. Reference | Related Articles | Metrics | Comments（0） Select A Framework of Convergence Analysis of Mini-batch Stochastic Projected Gradient Methods Jian Gu, Xian-Tao Xiao Journal of the Operations Research Society of China    2023, 11 (2): 347-369.   DOI: 10.1007/s40305-019-00276-7 Abstract （1003）      PDF       Knowledge map    Save In this paper, we establish a unified framework to study the almost sure global convergence and the expected convergencerates of a class ofmini-batch stochastic(projected) gradient (SG) methods, including two popular types of SG: stepsize diminished SG and batch size increased SG. We also show that the standard variance uniformly bounded assumption, which is frequently used in the literature to investigate the convergence of SG, is actually not required when the gradient of the objective function is Lipschitz continuous. Finally, we show that our framework can also be used for analyzing the convergence of a mini-batch stochastic extragradient method for stochastic variational inequality. Reference | Related Articles | Metrics | Comments（0） Select Approximate Customized Proximal Point Algorithms for Separable Convex Optimization Hong-Mei Chen, Xing-Ju Cai, Ling-Ling Xu Journal of the Operations Research Society of China    2023, 11 (2): 383-408.   DOI: 10.1007/s40305-022-00412-w Abstract （1049）      PDF       Knowledge map    Save Proximal point algorithm (PPA) is a useful algorithm framework and has good convergence properties. Themain difficulty is that the subproblems usually only have iterative solutions. In this paper, we propose an inexact customized PPA framework for twoblock separable convex optimization problem with linear constraint. We design two types of inexact error criteria for the subproblems. The first one is absolutely summable error criterion, under which both subproblems can be solved inexactly. When one of the two subproblems is easily solved, we propose another novel error criterion which is easier to implement, namely relative error criterion. The relative error criterion only involves one parameter, which is more implementable. We establish the global convergence and sub-linear convergence rate in ergodic sense for the proposed algorithms. The numerical experiments on LASSO regression problems and total variation-based image denoising problem illustrate that our new algorithms outperform the corresponding exact algorithms. Reference | Related Articles | Metrics | Comments（0） Select Optimized Filling of a Given Cuboid with Spherical Powders for Additive Manufacturing Zoya Duriagina, Igor Lemishka, Igor Litvinchev, Jose Antonio Marmolejo, Alexander Pankratov, Tatiana Romanova, Georgy Yaskov Journal of the Operations Research Society of China    2021, 9 (4): 853-868.   DOI: 10.1007/s40305-020-00314-9 Abstract （2206）      PDF       Knowledge map    Save In additive manufacturing (also known as 3D printing), a layer-by-layer buildup process is used for manufacturing parts. Modern laser 3D printers can work with various materials including metal powders. In particular, mixing various-sized spherical powders of titanium alloys is considered most promising for the aerospace industry. To achieve desired mechanical properties of the final product, it is necessary to maintain a certain proportional ratio between different powder fractions. In this paper, a modeling approach for filling up a rectangular 3D volume by unequal spheres in a layer-by-layer manner is proposed. A relative number of spheres of a given radius (relative frequency) are known and have to be fulfilled in the final packing. A fast heuristic has been developed to solve this special packing problem. Numerical results are compared with experimental findings for titanium alloy spherical powders. The relative frequencies obtained by using the imposed algorithm are very close to those obtained by the experiment. This provides an opportunity for using a cheap numerical modeling instead of expensive experimental study. Reference | Related Articles | Metrics | Comments（0） Select Nonuniqueness of Solutions of a Class of ℓ0-minimization Problems Jia-Liang Xu Journal of the Operations Research Society of China    2021, 9 (4): 893-908.   DOI: 10.1007/s40305-020-00336-3 Abstract （2199）      PDF       Knowledge map    Save Recently, finding the sparsest solution of an underdetermined linear system has become an important request in many areas such as compressed sensing, image processing, statistical learning, and data sparse approximation. In this paper, we study some theoretical properties of the solutions to a general class of $\ell_{0}$-minimization problems, which can be used to deal with many practical applications. We establish some necessary conditions for a point being the sparsest solution to this class of problems, and we also characterize the conditions for the multiplicity of the sparsest solutions to the problem. Finally, we discuss certain conditions for the boundedness of the solution set of this class of problems. Reference | Related Articles | Metrics | Comments（0） Select Carbon Emissions Abatement (CEA) Allocation Based on Inverse Slack-Based Model (SBM) Xiao-Yin Hu, Jian-Shu Li, Xiao-Ya Li, Jin-Chuan Cui Journal of the Operations Research Society of China    2021, 9 (3): 475-498.   DOI: 10.1007/s40305-020-00303-y Abstract （1419）      PDF       Knowledge map    Save Carbon emissions abatement (CEA) is an important issue that draws attention from both academicians and policymakers. Data envelopment analysis (DEA) has been a popular tool to allocate the CEA, and most previous works are based on radial DEA models. However, as shown in our paper, these models may give biased results due to their ignorance of slackness. To avoid such problems, we propose an allocation model based on the slack-based model and multiple-objective nonlinear programming to find the CEA allocation plan, which can minimize the GDP loss. The property of nonconvexity makes the model difficult to solve. Thus, we construct an approximation algorithm to solve this model with guaranteed error bounds and complexity. In the empirical application, we take regions of china as an illustrative example and find there is a significant region gap in China. Hence, we group the regions into eastern, central, and western, and give the main results, as well as the superiority of our allocation models compared with radial models. Reference | Related Articles | Metrics | Comments（0） Select Proximal Methods with Bregman Distances to Solve VIP on Hadamard Manifolds with Null Sectional Curvature Erik Alex Papa Quiroz, Paulo Roberto Oliveira Journal of the Operations Research Society of China    2021, 9 (3): 499-523.   DOI: 10.1007/s40305-020-00311-y Abstract （1330）      PDF       Knowledge map    Save We present an extension of the proximal point method with Bregman distances to solve variational inequality problems (VIP) on Hadamard manifolds with null sectional curvature. Under some natural assumptions, as for example, the existence of solutions of the VIP and the monotonicity of the multivalued vector field, we prove that the sequence of the iterates given by the method converges to a solution of the problem. Furthermore, this convergence is linear or superlinear with respect to the Bregman distance. Reference | Related Articles | Metrics | Comments（0） Select Data-driven Stochastic Programming with Distributionally Robust Constraints Under Wasserstein Distance: Asymptotic Properties Yu Mei, Zhi-Ping Chen, Bing-Bing Ji, Zhu-Jia Xu, Jia Liu Journal of the Operations Research Society of China    2021, 9 (3): 525-542.   DOI: 10.1007/s40305-020-00313-w Abstract （1350）      PDF       Knowledge map    Save Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown. We investigate a distributionally robust optimization problem with ambiguities in the objective function and countably infinite constraints. The ambiguity set is defined as a Wasserstein ball centered at the empirical distribution. Based on the concentration inequality of Wasserstein distance, we establish the asymptotic convergence property of the datadriven distributionally robust optimization problem when the sample size goes to infinity. We show that with probability 1, the optimal value and the optimal solution set of the data-driven distributionally robust problem converge to those of the stochastic optimization problem with true distribution. Finally, we provide numerical evidences for the established theoretical results. Reference | Related Articles | Metrics | Comments（0） Select Sparse Estimation of High-Dimensional Inverse Covariance Matrices with Explicit Eigenvalue Constraints Yun-Hai Xiao, Pei-Li Li, Sha Lu Journal of the Operations Research Society of China    2021, 9 (3): 543-568.   DOI: 10.1007/s40305-021-00351-y Abstract （1325）      PDF       Knowledge map    Save Firstly, this paper proposes a generalized log-determinant optimization model with the purpose of estimating the high-dimensional sparse inverse covariance matrices. Under the normality assumption, the zero components in the inverse covariance matrices represent the conditional independence between pairs of variables given all the other variables. The generalized model considered in this study, because of the setting of the eigenvalue bounded constraints, covers a large number of existing estimators as special cases. Secondly, rather than directly tracking the challenging optimization problem, this paper uses a couple of alternating direction methods of multipliers (ADMM) to solve its dual model where 5 separable structures are contained. The first implemented algorithm is based on a single Gauss-Seidel iteration, but it does not necessarily converge theoretically. In contrast, the second algorithm employs the symmetric Gauss-Seidel (sGS) based ADMM which is equivalent to the 2-block iterative scheme from the latest sGS decomposition theorem. Finally, we do numerical simulations using the synthetic data and the real data set which show that both algorithms are very effective in estimating high-dimensional sparse inverse covariance matrix. Reference | Related Articles | Metrics | Comments（0） Select Novel Global Optimization Algorithm with a Space-Filling Curve and Integral Function Zhong-Yu Wang, Yong-Jian Yang Journal of the Operations Research Society of China    2021, 9 (3): 619-640.   DOI: 10.1007/s40305-020-00294-w Abstract （1271）      PDF       Knowledge map    Save In this study, we consider the global optimization problem in a hypercube. We use a class of series to construct a curve in a hypercube, which can fill the hypercube, and we present an integral function on the curve. Based on the integral function, we propose an algorithm for solving the global optimization problem. Then, we perform a convergence analysis and numerical experiments to demonstrate the effectiveness of the proposed algorithm. Reference | Related Articles | Metrics | Comments（0） Select An Interior-Point Algorithm for Linear Programming with Optimal Selection of Centering Parameter and Step Size Ya-Guang Yang Journal of the Operations Research Society of China    2021, 9 (3): 659-671.   DOI: 10.1007/s40305-020-00312-x Abstract （1286）      PDF       Knowledge map    Save For interior-point algorithms in linear programming, it is well known that the selection of the centering parameter is crucial for proving polynomiality in theory and for efficiency in practice. However, the selection of the centering parameter is usually by heuristics and separated from the selection of the line-search step size. The heuristics are quite different while developing practically efficient algorithms, such as Mehrotra's predictor-corrector (MPC) algorithm, and theoretically efficient algorithms, such as short-step path-following algorithm. This introduces a dilemma that some algorithms with the best-known polynomial bound are least efficient in practice, and some most efficient algorithms may not be convergent in polynomial time. Therefore, in this paper, we propose a systematic way to optimally select the centering parameter and linesearch step size at the same time, and we show that the algorithm based on this strategy has the best-known polynomial bound and may be very efficient in computation for real problems. Reference | Related Articles | Metrics | Comments（0） Select Necessary Optimality Conditions for Semi-vectorial Bi-level Optimization with Convex Lower Level: Theoretical Results and Applications to the Quadratic Case Julien Collonge Journal of the Operations Research Society of China    2021, 9 (3): 691-712.   DOI: 10.1007/s40305-020-00305-w Abstract （1432）      PDF       Knowledge map    Save This paper explores related aspects to post-Pareto analysis arising from the multicriteria optimization problem. It consists of two main parts. In the first one, we give first-order necessary optimality conditions for a semi-vectorial bi-level optimization problem:the upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multi-objective optimization problem to be solved by several followers acting in a cooperative way (greatest coalition multi-players game). For the lower level, we deal with weakly or properly Pareto (efficient) solutions and we consider the so-called optimistic problem, i.e. when followers choose amongst Pareto solutions one which is the most favourable for the leader. In order to handle reallife applications, in the second part of the paper, we consider the case where each follower objective is expressed in a quadratic form. In this setting, we give explicit first-order necessary optimality conditions. Finally, some computational results are given to illustrate the paper. Reference | Related Articles | Metrics | Comments（0） Select Optimal Reinsurance and Investment Strategy with Delay in Heston’s SV Model Chun-Xiang A, Ai-Lin Gu, Yi Shao Journal of the Operations Research Society of China    2021, 9 (2): 245-271.   DOI: 10.1007/s40305-020-00331-8 Abstract （2218）      PDF       Knowledge map    Save In this paper, we consider an optimal investment and proportional reinsurance problem with delay, in which the insurer’s surplus process is described by a jump-diffusion model. The insurer can buy proportional reinsurance to transfer part of the insurance claims risk. In addition to reinsurance, she also can invests her surplus in a financial market, which is consisted of a risk-free asset and a risky asset described by Heston’s stochastic volatility (SV) model. Considering the performance-related capital flow, the insurer’s wealth process is modeled by a stochastic differential delay equation. The insurer’s target is to find the optimal investment and proportional reinsurance strategy to maximize the expected exponential utility of combined terminal wealth. We explicitly derive the optimal strategy and the value function. Finally, we provide some numerical examples to illustrate our results. Reference | Related Articles | Metrics | Comments（0） Select Inexact Operator Splitting Method for Monotone Inclusion Problems Yuan-Yuan Huang, Chang-He Liu, You-Lin Shang Journal of the Operations Research Society of China    2021, 9 (2): 274-306.   DOI: 10.1007/s40305-020-00296-8 Abstract （2149）      PDF       Knowledge map    Save The Douglas–Peaceman–Rachford–Varga operator splitting methods are a class of efficient methods for finding a zero of the sum of two maximal monotone operators in a real Hilbert space; however, they are sometimes difficult or even impossible to solve the subproblems exactly. In this paper, we suggest an inexact version in which some relative error criterion is discussed. The corresponding convergence properties are established, and some preliminary numerical experiments are reported to illustrate its efficiency. Reference | Related Articles | Metrics | Comments（0） Select Local Linear Convergence of an ADMM-Type Splitting Framework for Equality Constrained Optimization Jun-Feng Yang, Yin Zhang Journal of the Operations Research Society of China    2021, 9 (2): 308-319.   DOI: 10.1007/s40305-019-00271-y Abstract （2138）      PDF       Knowledge map    Save We establish local convergence results for a generic algorithmic framework for solving a wide class of equality constrained optimization problems. The framework is based on applying a splitting scheme to the augmented Lagrangian function that includes as a special case the well-known alternating direction method of multipliers (ADMM). Our local convergence analysis is free of the usual restrictions on ADMM-like methods, such as convexity, block separability or linearity of constraints. It offers a much-needed theoretical justification to the widespread practice of applying ADMM-like methods to nonconvex optimization problems. Reference | Related Articles | Metrics | Comments（0） Select Optimality and Duality for Multiobjective Semi-infinite Variational Problem Using Higher-Order B-type I Functions Promila Kumar, Jyoti Dagar Journal of the Operations Research Society of China    2021, 9 (2): 375-393.   DOI: 10.1007/s40305-019-00269-6 Abstract （2063）      PDF       Knowledge map    Save The notion of higher-order B-type I functional is introduced in this paper. This notion is utilized to study optimality and duality for multiobjective semi-infinite variational problem in which the index set of inequality constraints is an infinite set. The concept of efficiency is used as a tool for optimization. Mond–Weir type of dual is proposed for which weak, strong, and strict converse duality theorems are proved to relate efficient solutions of primal and dual problems. Reference | Related Articles | Metrics | Comments（0） Select An Adaptive Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition Xiao-Liang Dong, Zhi-Feng Dai, Reza Ghanbari, Xiang-Li Li Journal of the Operations Research Society of China    2021, 9 (2): 411-425.   DOI: 10.1007/s40305-019-00257-w Abstract （2345）      PDF       Knowledge map    Save In this paper, an adaptive three-term conjugate gradient method is proposed for solving unconstrained problems,which generates sufficient descent directions at each iteration. Different from the existent methods, a dynamical adjustment between Hestenes–Stiefel and Dai–Liao conjugacy conditions in our proposed method is developed. Under mild condition, we show that the proposed method converges globally. Numerical experimentation with the new method indicates that it efficiently solves the test problems and therefore is promising. Reference | Related Articles | Metrics | Comments（0） Select Two-Stage Stochastic Variational Inequalities: Theory, Algorithms and Applications Hai-Lin Sun, Xiao-Jun Chen Journal of the Operations Research Society of China    2021, 9 (1): 1-32.   DOI: 10.1007/s40305-019-00267-8 Abstract （1458）      PDF       Knowledge map    Save The stochastic variational inequality (SVI) provides a unified form of optimality conditions of stochastic optimization and stochastic games which have wide applications in science, engineering, economics and finance. In the recent two decades, one-stage SVI has been studied extensively and widely used in modeling equilibrium problems under uncertainty. Moreover, the recently proposed two-stage SVI and multistage SVI can be applied to the case when the decision makers want to make decisions at different stages in a stochastic environment. The two-stage SVI is a foundation of multistage SVI, which is to find a pair of “here-and-now” solution and “wait-and-see” solution. This paper provides a survey of recent developments in analysis, algorithms and applications of the two-stage SVI. Reference | Related Articles | Metrics | Comments（0） Select Continuity of Solutions for Parametric Set Optimization Problems via Scalarization Methods Pei-Pei Liu, Hong-Zhi Wei, Chun-Rong Chen, Sheng-Jie Li Journal of the Operations Research Society of China    2021, 9 (1): 79-97.   DOI: 10.1007/s40305-018-0230-6 Abstract （1334）      PDF       Knowledge map    Save The aim of this paper is to investigate the continuity of solution mappings for parametric set optimization problems with upper and lower set less order relations by scalarization methods. First, we recall some linear and nonlinear scalarization properties used to characterize the set order relations. Subsequently, we introduce new monotonicity concepts of the set-valued mapping by linear and nonlinear scalarization methods. Finally, we obtain the semicontinuity and closedness of solution mappings for parametric set optimization problems (both convex and nonconvex cases) under the monotonicity assumption and other suitable conditions. The results achieved do not impose the continuity of the set-valued objective mapping, which are obviously different from the related ones in the literature. Reference | Related Articles | Metrics | Comments（0） Select Generalized Krasnoselskii–Mann-Type Iteration for Nonexpansive Mappings in Banach Spaces You-Cai Zhang, Ke Guo, Tao Wang Journal of the Operations Research Society of China    2021, 9 (1): 195-206.   DOI: 10.1007/s40305-018-0235-1 Abstract （1395）      PDF       Knowledge map    Save The Krasnoselskii-Mann iteration plays an important role in the approximation of fixed points of nonexpansive mappings, and it is well known that the classic Krasnoselskii-Mann iteration is weakly convergent in Hilbert spaces. The weak convergence is also known even in Banach spaces. Recently, Kanzow and Shehu proposed a generalized Krasnoselskii-Mann-type iteration for nonexpansive mappings and established its convergence in Hilbert spaces. In this paper, we show that the generalized Krasnoselskii-Mann-type iteration proposed by Kanzow and Shehu also converges in Banach spaces. As applications, we proved the weak convergence of generalized proximal point algorithm in the uniformly convex Banach spaces. Reference | Related Articles | Metrics | Comments（0）

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