Journal of Global Optimization最新文献_第6页

Simple proximal-type algorithms for equilibrium problems 平衡问题的简单近似型算法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-03-14 DOI: 10.1007/s10898-024-01377-1

Yonghong Yao, Abubakar Adamu, Yekini Shehu, Jen-Chih Yao

引用次数: 0

A nonmonotone accelerated proximal gradient method with variable stepsize strategy for nonsmooth and nonconvex minimization problems 针对非光滑和非凸最小化问题的非单调加速近端梯度法与可变步长策略

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-03-05 DOI: 10.1007/s10898-024-01366-4

Hongwei Liu, Ting Wang, Zexian Liu

{"title":"A nonmonotone accelerated proximal gradient method with variable stepsize strategy for nonsmooth and nonconvex minimization problems","authors":"Hongwei Liu, Ting Wang, Zexian Liu","doi":"10.1007/s10898-024-01366-4","DOIUrl":"https://doi.org/10.1007/s10898-024-01366-4","url":null,"abstract":"In this paper, we consider the problem that minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting, which arising in many contemporary applications such as machine learning, statistics, and signal/image processing. To solve this problem, we propose a new nonmonotone accelerated proximal gradient method with variable stepsize strategy. Note that incorporating inertial term into proximal gradient method is a simple and efficient acceleration technique, while the descent property of the proximal gradient algorithm will lost. In our algorithm, the iterates generated by inertial proximal gradient scheme are accepted when the objective function values decrease or increase appropriately; otherwise, the iteration point is generated by proximal gradient scheme, which makes the function values on a subset of iterates are decreasing. We also introduce a variable stepsize strategy, which does not need a line search or does not need to know the Lipschitz constant and makes the algorithm easy to implement. We show that the sequence of iterates generated by the algorithm converges to a critical point of the objective function. Further, under the assumption that the objective function satisfies the Kurdyka–Łojasiewicz inequality, we prove the convergence rates of the objective function values and the iterates. Moreover, numerical results on both convex and nonconvex problems are reported to demonstrate the effectiveness and superiority of the proposed method and stepsize strategy.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"192 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140032824","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

Sketch-based multiplicative updating algorithms for symmetric nonnegative tensor factorizations with applications to face image clustering 基于草图的对称非负张量因子乘法更新算法及其在人脸图像聚类中的应用

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-03-01 DOI: 10.1007/s10898-024-01374-4

引用次数: 0

Computing the recession cone of a convex upper image via convex projection 通过凸投影计算凸上像的后退锥

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-03-01 DOI: 10.1007/s10898-023-01351-3

Gabriela Kováčová, Firdevs Ulus

引用次数: 0

A performance analysis of Basin hopping compared to established metaheuristics for global optimization Basin hopping 的性能分析：与已建立的元优化全局优化相比

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-28 DOI: 10.1007/s10898-024-01373-5

Marco Baioletti, Valentino Santucci, Marco Tomassini

{"title":"A performance analysis of Basin hopping compared to established metaheuristics for global optimization","authors":"Marco Baioletti, Valentino Santucci, Marco Tomassini","doi":"10.1007/s10898-024-01373-5","DOIUrl":"https://doi.org/10.1007/s10898-024-01373-5","url":null,"abstract":"During the last decades many metaheuristics for global numerical optimization have been proposed. Among them, Basin Hopping is very simple and straightforward to implement, although rarely used outside its original Physical Chemistry community. In this work, our aim is to compare Basin Hopping, and two population variants of it, with readily available implementations of the well known metaheuristics Differential Evolution, Particle Swarm Optimization, and Covariance Matrix Adaptation Evolution Strategy. We perform numerical experiments using the IOH profiler environment with the BBOB test function set and two difficult real-world problems. The experiments were carried out in two different but complementary ways: by measuring the performance under a fixed budget of function evaluations and by considering a fixed target value. The general conclusion is that Basin Hopping and its newly introduced population variant are almost as good as Covariance Matrix Adaptation on the synthetic benchmark functions and better than it on the two hard cluster energy minimization problems. Thus, the proposed analyses show that Basin Hopping can be considered a good candidate for global numerical optimization problems along with the more established metaheuristics, especially if one wants to obtain quick and reliable results on an unknown problem.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"914 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140005393","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

Fast deterministic algorithms for non-submodular maximization with strong performance guarantees 具有强大性能保证的非次模化最大化快速确定性算法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-22 DOI: 10.1007/s10898-024-01371-7

Cheng Lu, Wenguo Yang

引用次数: 0

A new dual-based cutting plane algorithm for nonlinear adjustable robust optimization 用于非线性可调鲁棒优化的新型基于对偶的切割面算法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-22 DOI: 10.1007/s10898-023-01360-2

{"title":"A new dual-based cutting plane algorithm for nonlinear adjustable robust optimization","authors":"","doi":"10.1007/s10898-023-01360-2","DOIUrl":"https://doi.org/10.1007/s10898-023-01360-2","url":null,"abstract":"<h3>Abstract</h3> This paper explores a class of nonlinear Adjustable Robust Optimization (ARO) problems, containing here-and-now and wait-and-see variables, with uncertainty in the objective function and constraints. By applying Fenchel’s duality on the wait-and-see variables, we obtain an equivalent dual reformulation, which is a nonlinear static robust optimization problem. Using the dual formulation, we provide conditions under which the ARO problem is convex on the here-and-now decision. Furthermore, since the dual formulation contains a non-concave maximization on the uncertain parameter, we use perspective relaxation and an alternating method to handle the non-concavity. By employing the perspective relaxation, we obtain an upper bound, which we show is the same as the static relaxation of the considered problem. Moreover, invoking the alternating method, we design a new dual-based cutting plane algorithm that is able to find a reasonable lower bound for the optimal objective value of the considered nonlinear ARO model. In addition to sketching and establishing the theoretical features of the algorithms, including convergence analysis, by numerical experiments we reveal the abilities of our cutting plane algorithm in producing locally robust solutions with an acceptable optimality gap.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"36 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139924360","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 criterion-space branch-reduction-bound algorithm for solving generalized multiplicative problems 解决广义乘法问题的准则空间分支还原约束算法

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-15 DOI: 10.1007/s10898-023-01358-w

Hongwei Jiao, Binbin Li, Wenqiang Yang

引用次数: 0

A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack 针对多维包的 K-means 支持强化学习框架

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-15 DOI: 10.1007/s10898-024-01364-6

Sabah Bushaj, İ. Esra Büyüktahtakın

{"title":"A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack","authors":"Sabah Bushaj, İ. Esra Büyüktahtakın","doi":"10.1007/s10898-024-01364-6","DOIUrl":"https://doi.org/10.1007/s10898-024-01364-6","url":null,"abstract":"In this paper, we address the difficulty of solving large-scale multi-dimensional knapsack instances (MKP), presenting a novel deep reinforcement learning (DRL) framework. In this DRL framework, we train different agents compatible with a discrete action space for sequential decision-making while still satisfying any resource constraint of the MKP. This novel framework incorporates the decision variable values in the 2D DRL where the agent is responsible for assigning a value of 1 or 0 to each of the variables. To the best of our knowledge, this is the first DRL model of its kind in which a 2D environment is formulated, and an element of the DRL solution matrix represents an item of the MKP. Our framework is configured to solve MKP instances of different dimensions and distributions. We propose a K-means approach to obtain an initial feasible solution that is used to train the DRL agent. We train four different agents in our framework and present the results comparing each of them with the CPLEX commercial solver. The results show that our agents can learn and generalize over instances with different sizes and distributions. Our DRL framework shows that it can solve medium-sized instances at least 45 times faster in CPU solution time and at least 10 times faster for large instances, with a maximum solution gap of 0.28% compared to the performance of CPLEX. Furthermore, at least 95% of the items are predicted in line with the CPLEX solution. Computations with DRL also provide a better optimality gap with respect to state-of-the-art approaches.","PeriodicalId":15961,"journal":{"name":"Journal of Global Optimization","volume":"121 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139759470","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

Regret analysis of an online majorized semi-proximal ADMM for online composite optimization 用于在线复合优化的在线主要半近似 ADMM 的遗憾分析

IF 1.8 3区数学

Journal of Global Optimization Pub Date : 2024-02-15 DOI: 10.1007/s10898-024-01365-5

Zehao Xiao, Liwei Zhang

引用次数: 0