Computational Optimization and Applications最新文献_第3页

T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization 用三阶张量对受约束多项式优化进行 T-半无限编程放松

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-06-02 DOI: 10.1007/s10589-024-00582-8

Hiroki Marumo, Sunyoung Kim, Makoto Yamashita

引用次数: 0

Delayed Weighted Gradient Method with simultaneous step-sizes for strongly convex optimization 采用同步步长的延迟加权梯度法进行强凸优化

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-05-31 DOI: 10.1007/s10589-024-00586-4

Hugo Lara, Rafael Aleixo, Harry Oviedo

引用次数: 0

A non-monotone trust-region method with noisy oracles and additional sampling 具有噪声信标和额外采样的非单调信任区域方法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-05-31 DOI: 10.1007/s10589-024-00580-w

Nataša Krejić, Nataša Krklec Jerinkić, Ángeles Martínez, Mahsa Yousefi

{"title":"A non-monotone trust-region method with noisy oracles and additional sampling","authors":"Nataša Krejić, Nataša Krklec Jerinkić, Ángeles Martínez, Mahsa Yousefi","doi":"10.1007/s10589-024-00580-w","DOIUrl":"https://doi.org/10.1007/s10589-024-00580-w","url":null,"abstract":"In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the unconstrained, nonlinear, and non-convex optimization problems arising in the training of deep neural networks. The proposed algorithm makes use of subsampling strategies that yield noisy approximations of the finite sum objective function and its gradient. We introduce an adaptive sample size strategy based on inexpensive additional sampling to control the resulting approximation error. Depending on the estimated progress of the algorithm, this can yield sample size scenarios ranging from mini-batch to full sample functions. We provide convergence analysis for all possible scenarios and show that the proposed method achieves almost sure convergence under standard assumptions for the trust-region framework. We report numerical experiments showing that the proposed algorithm outperforms its state-of-the-art counterpart in deep neural network training for image classification and regression tasks while requiring a significantly smaller number of gradient evaluations.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141195413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 boosted DC algorithm for non-differentiable DC components with non-monotone line search 采用非单调线搜索的无差别直流分量提升直流算法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-05-11 DOI: 10.1007/s10589-024-00578-4

O. P. Ferreira, E. M. Santos, J. C. O. Souza

{"title":"A boosted DC algorithm for non-differentiable DC components with non-monotone line search","authors":"O. P. Ferreira, E. M. Santos, J. C. O. Souza","doi":"10.1007/s10589-024-00578-4","DOIUrl":"https://doi.org/10.1007/s10589-024-00578-4","url":null,"abstract":"We introduce a new approach to apply the boosted difference of convex functions algorithm (BDCA) for solving non-convex and non-differentiable problems involving difference of two convex functions (DC functions). Supposing the first DC component differentiable and the second one possibly non-differentiable, the main idea of BDCA is to use the point computed by the subproblem of the DC algorithm (DCA) to define a descent direction of the objective from that point, and then a monotone line search starting from it is performed in order to find a new point which decreases the objective function when compared with the point generated by the subproblem of DCA. This procedure improves the performance of the DCA. However, if the first DC component is non-differentiable, then the direction computed by BDCA can be an ascent direction and a monotone line search cannot be performed. Our approach uses a non-monotone line search in the BDCA (nmBDCA) to enable a possible growth in the objective function values controlled by a parameter. Under suitable assumptions, we show that any cluster point of the sequence generated by the nmBDCA is a critical point of the problem under consideration and provides some iteration-complexity bounds. Furthermore, if the first DC component is differentiable, we present different iteration-complexity bounds and prove the full convergence of the sequence under the Kurdyka–Łojasiewicz property of the objective function. Some numerical experiments show that the nmBDCA outperforms the DCA, such as its monotone version.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

An away-step Frank–Wolfe algorithm for constrained multiobjective optimization 用于约束性多目标优化的远离步骤弗兰克-沃尔夫算法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-05-07 DOI: 10.1007/s10589-024-00577-5

Douglas S. Gonçalves, Max L. N. Gonçalves, Jefferson G. Melo

引用次数: 0

Shape optimization for interface identification in nonlocal models 非局部模型界面识别的形状优化

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-05-07 DOI: 10.1007/s10589-024-00575-7

Matthias Schuster, Christian Vollmann, Volker Schulz

引用次数: 0

A hybrid inexact regularized Newton and negative curvature method 不精确正则化牛顿和负曲率混合方法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-05-06 DOI: 10.1007/s10589-024-00576-6

Hong Zhu, Yunhai Xiao

{"title":"A hybrid inexact regularized Newton and negative curvature method","authors":"Hong Zhu, Yunhai Xiao","doi":"10.1007/s10589-024-00576-6","DOIUrl":"https://doi.org/10.1007/s10589-024-00576-6","url":null,"abstract":"In this paper, we propose a hybrid inexact regularized Newton and negative curvature method for solving unconstrained nonconvex problems. The descent direction is chosen based on different conditions, either the negative curvature or the inexact regularized direction. In addition, to minimize computational costs while obtaining the negative curvature, we employ a dimensionality reduction strategy to verify if the Hessian matrix exhibits negative curvatures within a three-dimensional subspace. We show that the proposed method can achieve the best-known global iteration complexity if the Hessian of the objective function is Lipschitz continuous on a certain compact set. Two simplified methods for nonconvex and strongly convex problems are analyzed as specific instances of the proposed method. We show that under the local error bound assumption with respect to the gradient, the distance between iterations generated by our proposed method and the local solution set converges to (0) at a superlinear rate. Additionally, for strongly convex problems, the quadratic convergence rate can be achieved. Extensive numerical experiments show the effectiveness of the proposed method.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Chance-constrained programs with convex underlying functions: a bilevel convex optimization perspective 具有凸基础函数的机会受限程序：双层凸优化视角

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-04-27 DOI: 10.1007/s10589-024-00573-9

Yassine Laguel, Jérôme Malick, Wim van Ackooij

引用次数: 0

An inexactly accelerated algorithm for nonnegative tensor CP decomposition with the column unit constraints 带有列单位约束的非负张量 CP 分解的非精确加速算法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-04-25 DOI: 10.1007/s10589-024-00574-8

Zihao Wang, Minru Bai

引用次数: 0

Stochastic average model methods 随机平均模型方法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-04-24 DOI: 10.1007/s10589-024-00563-x

Matt Menickelly, Stefan M. Wild

引用次数: 0