Journal of Global Optimization最新文献

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Robust second order cone conditions and duality for multiobjective problems under uncertainty data 不确定数据下多目标问题的稳健二阶锥条件和对偶性
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-01-22 DOI: 10.1007/s10898-023-01335-3
Cao Thanh Tinh, Thai Doan Chuong
{"title":"Robust second order cone conditions and duality for multiobjective problems under uncertainty data","authors":"Cao Thanh Tinh, Thai Doan Chuong","doi":"10.1007/s10898-023-01335-3","DOIUrl":"https://doi.org/10.1007/s10898-023-01335-3","url":null,"abstract":"<p>This paper studies a class of multiobjective convex polynomial problems, where both the constraint and objective functions involve uncertain parameters that reside in ellipsoidal uncertainty sets. Employing the robust deterministic approach, we provide necessary conditions and sufficient conditions, which are exhibited in relation to second order cone conditions, for robust (weak) Pareto solutions of the uncertain multiobjective optimization problem. A dual multiobjective problem is proposed to examine robust converse, robust weak and robust strong duality relations between the primal and dual problems. Moreover, we establish robust solution relationships between the uncertain multiobjective optimization program and a (scalar) second order cone programming relaxation problem of a corresponding weighted-sum optimization problem. This in particular shows that we can find a robust (weak) Pareto solution of the uncertain multiobjective optimization problem by solving a second order cone programming relaxation.\u0000</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139518645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Single-lot, lot-streaming problem for a 1 + m hybrid flow shop 1 + m 混合流水车间的单批次、批次流水问题
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-01-12 DOI: 10.1007/s10898-023-01354-0
Sanchit Singh, Subhash C. Sarin, Ming Cheng
{"title":"Single-lot, lot-streaming problem for a 1 + m hybrid flow shop","authors":"Sanchit Singh, Subhash C. Sarin, Ming Cheng","doi":"10.1007/s10898-023-01354-0","DOIUrl":"https://doi.org/10.1007/s10898-023-01354-0","url":null,"abstract":"<p>In this paper, we consider an application of lot-streaming for processing a lot of multiple items in a hybrid flow shop (HFS) for the objective of minimizing makespan. The HFS that we consider consists of two stages with a single machine available for processing in Stage 1 and <i>m</i> identical parallel machines in Stage 2. We call this problem a 1 + <i>m</i> TSHFS-LSP (two-stage hybrid flow shop, lot streaming problem), and show it to be NP-hard in general, except for the case when the sublot sizes are treated to be continuous. The novelty of our work is in obtaining closed-form expressions for optimal continuous sublot sizes that can be solved in polynomial time, for a given number of sublots. A fast linear search algorithm is also developed for determining the optimal number of sublots for the case of continuous sublot sizes. For the case when the sublot sizes are discrete, we propose a branch-and-bound-based heuristic to determine both the number of sublots and sublot sizes and demonstrate its efficacy by comparing its performance against that of a direct solution of a mixed-integer formulation of the problem by CPLEX<sup>®</sup>.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"2 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139458859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On semidefinite programming relaxations for a class of robust SOS-convex polynomial optimization problems 关于一类鲁棒 SOS-凸多项式优化问题的半有限编程松弛
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-01-06 DOI: 10.1007/s10898-023-01353-1
Xiangkai Sun, Jiayi Huang, Kok Lay Teo
{"title":"On semidefinite programming relaxations for a class of robust SOS-convex polynomial optimization problems","authors":"Xiangkai Sun, Jiayi Huang, Kok Lay Teo","doi":"10.1007/s10898-023-01353-1","DOIUrl":"https://doi.org/10.1007/s10898-023-01353-1","url":null,"abstract":"<p>In this paper, we deal with a new class of SOS-convex (sum of squares convex) polynomial optimization problems with spectrahedral uncertainty data in both the objective and constraints. By using robust optimization and a weighted-sum scalarization methodology, we first present the relationship between robust solutions of this uncertain SOS-convex polynomial optimization problem and that of its corresponding scalar optimization problem. Then, by using a normal cone constraint qualification condition, we establish necessary and sufficient optimality conditions for robust weakly efficient solutions of this uncertain SOS-convex polynomial optimization problem based on scaled diagonally dominant sums of squares conditions and linear matrix inequalities. Moreover, we introduce a semidefinite programming relaxation problem of its weighted-sum scalar optimization problem, and show that robust weakly efficient solutions of the uncertain SOS-convex polynomial optimization problem can be found by solving the corresponding semidefinite programming relaxation problem.\u0000</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"206 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139373847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral projected subgradient method with a 1-memory momentum term for constrained multiobjective optimization problem 针对受约束多目标优化问题的带 1 个内存动量项的频谱投射子梯度法
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-01-05 DOI: 10.1007/s10898-023-01349-x
Jing-jing Wang, Li-ping Tang, Xin-min Yang
{"title":"Spectral projected subgradient method with a 1-memory momentum term for constrained multiobjective optimization problem","authors":"Jing-jing Wang, Li-ping Tang, Xin-min Yang","doi":"10.1007/s10898-023-01349-x","DOIUrl":"https://doi.org/10.1007/s10898-023-01349-x","url":null,"abstract":"<p>In this paper, we propose a spectral projected subgradient method with a 1-memory momentum term for solving constrained convex multiobjective optimization problem. This method combines the subgradient-type algorithm for multiobjective optimization problems with the idea of the spectral projected algorithm to accelerate the convergence process. Additionally, a 1-memory momentum term is added to the subgradient direction in the early iterations. The 1-memory momentum term incorporates, in the present iteration, some of the influence of the past iterations, and this can help to improve the search direction. Under suitable assumptions, we show that the sequence generated by the method converges to a weakly Pareto efficient solution and derive the sublinear convergence rates for the proposed method. Finally, computational experiments are given to demonstrate the effectiveness of the proposed method.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"31 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139373808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The exact projective penalty method for constrained optimization 约束优化的精确投影惩罚法
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-01-03 DOI: 10.1007/s10898-023-01350-4
{"title":"The exact projective penalty method for constrained optimization","authors":"","doi":"10.1007/s10898-023-01350-4","DOIUrl":"https://doi.org/10.1007/s10898-023-01350-4","url":null,"abstract":"<h3>Abstract</h3> <p>A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing its value at the projection of an infeasible point on the feasible set with the distance to the projection. Beside Euclidean projections, also a pointed projection in the direction of some fixed internal feasible point can be used. The equivalence means that local and global minimums of the problems coincide. Nonconvex sets with multivalued Euclidean projections are admitted, and the objective function may be lower semicontinuous. The particular case of convex problems is included. The obtained unconstrained or box constrained problem is solved by a version of the branch and bound method combined with local optimization. In principle, any local optimizer can be used within the branch and bound scheme but in numerical experiments sequential quadratic programming method was successfully used. So the proposed exact penalty method does not assume the existence of the objective function outside the allowable area and does not require the selection of the penalty coefficient.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"30 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139093752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Constrained multiobjective optimization of expensive black-box functions using a heuristic branch-and-bound approach 使用启发式分支和边界方法对昂贵的黑盒子函数进行有约束的多目标优化
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-01-02 DOI: 10.1007/s10898-023-01336-2
{"title":"Constrained multiobjective optimization of expensive black-box functions using a heuristic branch-and-bound approach","authors":"","doi":"10.1007/s10898-023-01336-2","DOIUrl":"https://doi.org/10.1007/s10898-023-01336-2","url":null,"abstract":"<h3>Abstract</h3> <p>While constrained, multiobjective optimization is generally very difficult, there is a special case in which such problems can be solved with a simple, elegant branch-and-bound algorithm. This special case is when the objective and constraint functions are Lipschitz continuous with known Lipschitz constants. Given these Lipschitz constants, one can compute lower bounds on the functions over subregions of the search space. This allows one to iteratively partition the search space into rectangles, deleting those rectangles which—based on the lower bounds—contain points that are all provably infeasible or provably dominated by previously sampled point(s). As the algorithm proceeds, the rectangles that have not been deleted provide a tight covering of the Pareto set in the input space. Unfortunately, for black-box optimization this elegant algorithm cannot be applied, as we would not know the Lipschitz constants. In this paper, we show how one can heuristically extend this branch-and-bound algorithm to the case when the problem functions are black-box using an approach similar to that used in the well-known DIRECT global optimization algorithm. We call the resulting method “simDIRECT.” Initial experience with simDIRECT on test problems suggests that it performs similar to, or better than, multiobjective evolutionary algorithms when solving problems with small numbers of variables (up to 12) and a limited number of runs (up to 600). </p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139080250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Determining solution set of nonlinear inequalities using space-filling curves for finding working spaces of planar robots 利用空间填充曲线确定非线性不等式的解集,以寻找平面机器人的工作空间
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-01-02 DOI: 10.1007/s10898-023-01352-2
Daniela Lera, Maria Chiara Nasso, Mikhail Posypkin, Yaroslav D. Sergeyev
{"title":"Determining solution set of nonlinear inequalities using space-filling curves for finding working spaces of planar robots","authors":"Daniela Lera, Maria Chiara Nasso, Mikhail Posypkin, Yaroslav D. Sergeyev","doi":"10.1007/s10898-023-01352-2","DOIUrl":"https://doi.org/10.1007/s10898-023-01352-2","url":null,"abstract":"<p>In this paper, the problem of approximating and visualizing the solution set of systems of nonlinear inequalities is considered. It is supposed that left-hand parts of the inequalities can be multiextremal and non-differentiable. Thus, traditional local methods using gradients cannot be applied in these circumstances. Problems of this kind arise in many scientific applications, in particular, in finding working spaces of robots where it is necessary to determine not one but <i>all</i> the solutions of the system of nonlinear inequalities. Global optimization algorithms can be taken as an inspiration for developing methods for solving this problem. In this article, two new methods using two different approximations of Peano–Hilbert space-filling curves actively used in global optimization are proposed. Convergence conditions of the new methods are established. Numerical experiments executed on problems regarding finding the working spaces of several robots show a promising performance of the new algorithms.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"29 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139077175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
DC-programming for neural network optimizations 神经网络优化的直流编程
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-01-02 DOI: 10.1007/s10898-023-01344-2
{"title":"DC-programming for neural network optimizations","authors":"","doi":"10.1007/s10898-023-01344-2","DOIUrl":"https://doi.org/10.1007/s10898-023-01344-2","url":null,"abstract":"<h3>Abstract</h3> <p>We discuss two key problems related to learning and optimization of neural networks: the computation of the adversarial attack for adversarial robustness and approximate optimization of complex functions. We show that both problems can be cast as instances of DC-programming. We give an explicit decomposition of the corresponding functions as differences of convex functions (DC) and report the results of experiments demonstrating the effectiveness of the DCA algorithm applied to these problems. </p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"25 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139080275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Extragradient-type methods with $$mathcal {O}left( 1/kright) $$ last-iterate convergence rates for co-hypomonotone inclusions 具有$$mathcal {O}left( 1/kright) $$共hypomonotone 内含物最后迭代收敛率的外梯度型方法
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2023-12-16 DOI: 10.1007/s10898-023-01347-z
Quoc Tran-Dinh
{"title":"Extragradient-type methods with $$mathcal {O}left( 1/kright) $$ last-iterate convergence rates for co-hypomonotone inclusions","authors":"Quoc Tran-Dinh","doi":"10.1007/s10898-023-01347-z","DOIUrl":"https://doi.org/10.1007/s10898-023-01347-z","url":null,"abstract":"<p>We develop two “Nesterov’s accelerated” variants of the well-known extragradient method to approximate a solution of a co-hypomonotone inclusion constituted by the sum of two operators, where one is Lipschitz continuous and the other is possibly multivalued. The first scheme can be viewed as an accelerated variant of Tseng’s forward-backward-forward splitting (FBFS) method, while the second one is a Nesterov’s accelerated variant of the “past” FBFS scheme, which requires only one evaluation of the Lipschitz operator and one resolvent of the multivalued mapping. Under appropriate conditions on the parameters, we theoretically prove that both algorithms achieve <span>(mathcal {O}left( 1/kright) )</span> last-iterate convergence rates on the residual norm, where <i>k</i> is the iteration counter. Our results can be viewed as alternatives of a recent class of Halpern-type methods for root-finding problems. For comparison, we also provide a new convergence analysis of the two recent extra-anchored gradient-type methods for solving co-hypomonotone inclusions.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"7 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Bregman inertial forward-reflected-backward method for nonconvex minimization 用于非凸最小化的布雷格曼惯性前向-反射-后向方法
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2023-12-16 DOI: 10.1007/s10898-023-01348-y
Xianfu Wang, Ziyuan Wang
{"title":"A Bregman inertial forward-reflected-backward method for nonconvex minimization","authors":"Xianfu Wang, Ziyuan Wang","doi":"10.1007/s10898-023-01348-y","DOIUrl":"https://doi.org/10.1007/s10898-023-01348-y","url":null,"abstract":"<p>We propose a Bregman inertial forward-reflected-backward (BiFRB) method for nonconvex composite problems. Assuming the generalized concave Kurdyka-Łojasiewicz property, we obtain sequential convergence of BiFRB, as well as convergence rates on both the function value and actual sequence. One distinguishing feature in our analysis is that we utilize a careful treatment of merit function parameters, circumventing the usual restrictive assumption on the inertial parameters. We also present formulae for the Bregman subproblem, supplementing not only BiFRB but also the work of Boţ-Csetnek-László and Boţ-Csetnek. Numerical simulations are conducted to evaluate the performance of our proposed algorithm.\u0000</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"8 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138681761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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