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Journal of Global Optimization最新文献

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Novel algorithms based on forward-backward splitting technique: effective methods for regression and classification 基于前向-后向分割技术的新算法：回归和分类的有效方法
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-08-07 DOI: 10.1007/s10898-024-01425-w
Yunus Atalan, Emirhan Hacıoğlu, Müzeyyen Ertürk, Faik Gürsoy, Gradimir V. Milovanović
{"title":"Novel algorithms based on forward-backward splitting technique: effective methods for regression and classification","authors":"Yunus Atalan, Emirhan Hacıoğlu, Müzeyyen Ertürk, Faik Gürsoy, Gradimir V. Milovanović","doi":"10.1007/s10898-024-01425-w","DOIUrl":"https://doi.org/10.1007/s10898-024-01425-w","url":null,"abstract":"<p>In this paper, we introduce two novel forward-backward splitting algorithms (FBSAs) for nonsmooth convex minimization. We provide a thorough convergence analysis, emphasizing the new algorithms and contrasting them with existing ones. Our findings are validated through a numerical example. The practical utility of these algorithms in real-world applications, including machine learning for tasks such as classification, regression, and image deblurring reveal that these algorithms consistently approach optimal solutions with fewer iterations, highlighting their efficiency in real-world scenarios.\u0000</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942917","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
Robust bilevel optimization for near-optimal lower-level solutions 近乎最优下层解决方案的稳健双层优化
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-07-30 DOI: 10.1007/s10898-024-01422-z
Mathieu Besançon, Miguel F. Anjos, Luce Brotcorne
{"title":"Robust bilevel optimization for near-optimal lower-level solutions","authors":"Mathieu Besançon, Miguel F. Anjos, Luce Brotcorne","doi":"10.1007/s10898-024-01422-z","DOIUrl":"https://doi.org/10.1007/s10898-024-01422-z","url":null,"abstract":"<p>Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution feasibility from limited deviations from the optimal solution at the lower level. General properties and necessary conditions for the existence of solutions are derived for near-optimal robust versions of general bilevel optimization problems. A duality-based solution method is defined when the lower level is convex, leveraging the methodology from the robust and bilevel literature. Numerical results assess the efficiency of exact and heuristic methods and the impact of valid inequalities on the solution time.\u0000</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867617","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
Strong convergence of the composition of firmly nonexpansive mappings 坚定非展开映射组成的强收敛性
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-07-27 DOI: 10.1007/s10898-024-01417-w
José Márcio Machado de Brito, João Xavier da Cruz Neto, Ítalo Dowell Lira Melo
{"title":"Strong convergence of the composition of firmly nonexpansive mappings","authors":"José Márcio Machado de Brito, João Xavier da Cruz Neto, Ítalo Dowell Lira Melo","doi":"10.1007/s10898-024-01417-w","DOIUrl":"https://doi.org/10.1007/s10898-024-01417-w","url":null,"abstract":"<p>In this paper, we provide a necessary and sufficient condition under which the compositions of finitely many firmly nonexpansive mappings in a <i>p</i>-uniformly convex space converge strongly. In particular, we obtain convergence results for the method of alternating projections in CAT(<span>(kappa )</span>) spaces, with <span>(kappa ge 0)</span>. We also study the rate of convergence of the sequence generated by the method in cases where the firmly nonexpansive mappings satisfy an error bound, and the set of fixed points of these mappings is boundedly linearly regular.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141770711","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
Approximation algorithms for solving the vertex-traversing-constrained mixed Chinese postman problem 求解顶点遍历受限混合中国邮差问题的近似算法
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-07-22 DOI: 10.1007/s10898-024-01420-1
Pengxiang Pan, Junran Lichen, Jianping Li
{"title":"Approximation algorithms for solving the vertex-traversing-constrained mixed Chinese postman problem","authors":"Pengxiang Pan, Junran Lichen, Jianping Li","doi":"10.1007/s10898-024-01420-1","DOIUrl":"https://doi.org/10.1007/s10898-024-01420-1","url":null,"abstract":"<p>In this paper, we address the vertex-traversing-constrained mixed Chinese postman problem (the VtcMCP problem), which is a further generalization of the Chinese postman problem, and this new problem has many practical applications in real life. Specifically, given a connected mixed graph <span>(G=(V, Ecup A; w,b))</span> with length function <span>(w(cdot ))</span> on edges and arcs and traversal function <span>(b(cdot ))</span> on vertices, we are asked to determine a tour traversing each link (i.e., either edge or arc) at least once and each vertex <i>v</i> at most <i>b</i>(<i>v</i>) times, the objective is to minimize the total length of such a tour, where <span>(n=|V|)</span> is the number of vertices and <span>(m=|Ecup A|)</span> is the number of links of <i>G</i>, respectively. We obtain the following four main results. (1) Given any two constants <span>(beta ge 1)</span> and <span>(alpha ge 1)</span>, we prove that there is no polynomial-time algorithm with approximation ratios <span>((1,beta ))</span> or <span>((alpha , 1))</span> for solving the VtcMCP problem, where an (<i>h</i>, <i>k</i>)-approximation algorithm for solving the VtcMCP problem is one algorithm that produces a solution with violating the vertex-traversing constraints by at most a ratio of <i>h</i> and with costing at most <i>k</i> times the optimal value; (2) We design a (3, 2)-approximation algorithm <span>({{mathcal {A}}})</span> to solve the VtcMCP problem in time <span>(O(m^{2}log n))</span>; (3) We prove the fact that this algorithm <span>({{mathcal {A}}})</span> in (2) is indeed an exact algorithm to optimally solve the VtcMCP problem for the case <span>(E=emptyset )</span>; (4) We present an exact algorithm to optimally solve the VtcMCP problem in time <span>(O(m^{3}))</span> for the case <span>(A=emptyset )</span>.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744855","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
Hierarchy relaxations for robust equilibrium constrained polynomial problems and applications to electric vehicle charging scheduling 稳健均衡约束多项式问题的层次松弛及在电动汽车充电调度中的应用
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-07-20 DOI: 10.1007/s10898-024-01421-0
Thai Doan Chuong, Xinghuo Yu, Andrew Eberhard, Chaojie Li, Chen Liu
{"title":"Hierarchy relaxations for robust equilibrium constrained polynomial problems and applications to electric vehicle charging scheduling","authors":"Thai Doan Chuong, Xinghuo Yu, Andrew Eberhard, Chaojie Li, Chen Liu","doi":"10.1007/s10898-024-01421-0","DOIUrl":"https://doi.org/10.1007/s10898-024-01421-0","url":null,"abstract":"<p>In this paper, we consider a polynomial problem with equilibrium constraints in which the constraint functions and the equilibrium constraints involve data uncertainties. Employing a robust optimization approach, we examine the uncertain equilibrium constrained polynomial optimization problem by establishing lower bound approximations and asymptotic convergences of bounded degree diagonally dominant sum-of-squares (DSOS), scaled diagonally dominant sum-of-squares (SDSOS) and sum-of-squares (SOS) polynomial relaxations for the robust equilibrium constrained polynomial optimization problem. We also provide numerical examples to illustrate how the optimal value of a robust equilibrium constrained problem can be calculated by solving associated relaxation problems. Furthermore, an application to electric vehicle charging scheduling problems under uncertain discharging supplies shows that for the lower relaxation degrees, the DSOS, SDSOS and SOS relaxations obtain reasonable charging costs and for the higher relaxation degrees, the SDSOS relaxation scheme has the best performance, making it desirable for practical applications.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745013","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 method based on parametric convex programming for solving convex multiplicative programming problem 基于参数凸编程的凸乘法编程问题求解方法
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-07-18 DOI: 10.1007/s10898-024-01416-x
Yunchol Jong, Yongjin Kim, Hyonchol Kim
{"title":"A method based on parametric convex programming for solving convex multiplicative programming problem","authors":"Yunchol Jong, Yongjin Kim, Hyonchol Kim","doi":"10.1007/s10898-024-01416-x","DOIUrl":"https://doi.org/10.1007/s10898-024-01416-x","url":null,"abstract":"<p>We propose a new parametric approach to convex multiplicative programming problem. This problem is nonconvex optimization problem with a lot of practical applications. Compared with preceding methods based on branch-and-bound procedure and other approaches, the idea of our method is to reduce the original nonconvex problem to a parametric convex programming problem having parameters in objective functions. To find parameters corresponding to the optimal solution of the original problem, a system of nonlinear equations which the parameters should satisfy is studied. Then, the system is solved by a Newton-like algorithm, which needs to solve a convex programming problem in each iteration and has global linear and local superlinear/quadratic rate of convergence under some assumptions. Moreover, under some mild assumptions, our algorithm has a finite convergence, that is, the algorithm finds a solution after a finite number of iterations. The numerical results show that our method has much better performance than other reported methods for this class of problems.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744856","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 Two-Step Proximal Point Algorithm for Nonconvex Equilibrium Problems with Applications to Fractional Programming 非凸均衡问题的两步近点算法及其在分式编程中的应用
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-07-17 DOI: 10.1007/s10898-024-01419-8
Alfredo Iusem, Felipe Lara, Raúl T. Marcavillaca, Le Hai Yen
{"title":"A Two-Step Proximal Point Algorithm for Nonconvex Equilibrium Problems with Applications to Fractional Programming","authors":"Alfredo Iusem, Felipe Lara, Raúl T. Marcavillaca, Le Hai Yen","doi":"10.1007/s10898-024-01419-8","DOIUrl":"https://doi.org/10.1007/s10898-024-01419-8","url":null,"abstract":"<p>We present a proximal point type algorithm tailored for tackling pseudomonotone equilibrium problems in a Hilbert space which are not necessarily convex in the second argument of the involved bifunction. Motivated by the extragradient algorithm, we propose a two-step method and we prove that the generated sequence converges strongly to a solution of the nonconvex equilibrium problem under mild assumptions and, also, we establish a linear convergent rate for the iterates. Furthermore, we identify a new class of functions that meet our assumptions, and we provide sufficient conditions for quadratic fractional functions to exhibit strong quasiconvexity. Finally, we perform numerical experiments comparing our algorithm against two alternative methods for classes of nonconvex mixed variational inequalities.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719223","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 generalized alternating direction implicit method for consensus optimization: application to distributed sparse logistic regression 共识优化的广义交替方向隐含法：应用于分布式稀疏逻辑回归
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-07-16 DOI: 10.1007/s10898-024-01418-9
Weiyang Ding, Michael K. Ng, Wenxing Zhang
{"title":"A generalized alternating direction implicit method for consensus optimization: application to distributed sparse logistic regression","authors":"Weiyang Ding, Michael K. Ng, Wenxing Zhang","doi":"10.1007/s10898-024-01418-9","DOIUrl":"https://doi.org/10.1007/s10898-024-01418-9","url":null,"abstract":"","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141642183","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
Modified general splitting method for the split feasibility problem 分割可行性问题的修正一般分割法
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-07-10 DOI: 10.1007/s10898-024-01399-9
Seakweng Vong, Zhongsheng Yao
{"title":"Modified general splitting method for the split feasibility problem","authors":"Seakweng Vong, Zhongsheng Yao","doi":"10.1007/s10898-024-01399-9","DOIUrl":"https://doi.org/10.1007/s10898-024-01399-9","url":null,"abstract":"<p>Based on the equivalent optimization problems of the splitting feasibility problem, we investigate this problem by using modified general splitting method in this paper. One is a relaxation splitting method with linearization, and the other combines the former with alternated inertial extrapolation step. The strong convergence of our algorithms is analyzed when related parameters are properly chosen. Compared with most existing results where inertial factor must be less than 1, inertial factor can be taken 1 in our alternated inertial-type algorithm. The efficiency of our methods are illustrated by some numerical examples.\u0000</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567633","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
Optimality analysis for $$epsilon $$ -quasi solutions of optimization problems via $$epsilon $$ -upper convexificators: a dual approach 通过 $$epsilon $$ -upper convexificators 对优化问题的 $$epsilon $$ -quasi 解进行最优性分析：一种对偶方法
IF 1.8 3区 数学
Journal of Global Optimization Pub Date : 2024-07-08 DOI: 10.1007/s10898-024-01415-y
Tran Van Su
{"title":"Optimality analysis for $$epsilon $$ -quasi solutions of optimization problems via $$epsilon $$ -upper convexificators: a dual approach","authors":"Tran Van Su","doi":"10.1007/s10898-024-01415-y","DOIUrl":"https://doi.org/10.1007/s10898-024-01415-y","url":null,"abstract":"<p>The theory of duality is of fundamental importance in the study of vector optimization problems and vector equilibrium problems. A Mond–Weir-type dual model for such problems is important in practice. Therefore, studying such problems with a dual approach is really useful and necessary in the literature. The goal of this article is to formulate Mond–Weir-type dual models for the minimization problem (P), the constrained vector optimization problem (CVOP) and the constrained vector equilibrium problem (CVEP) in terms of <span>(epsilon )</span>-upper convexificators. By applying the concept of <span>(epsilon )</span>-pseudoconvexity, some weak, strong and converse duality theorems for the primal problem (P) and its dual problem (DP), the primal vector optimization problem (CVOP) and its Mond–Weir-type dual problem (MWCVOP), the primal vector equilibrium problem (P) and its Mond–Weir-type dual problem (MWCVEP) are explored.</p>","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567635","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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