Computational Optimization and Applications最新文献

A family of conjugate gradient methods with guaranteed positiveness and descent for vector optimization 保证正向性和下降的共轭梯度法系列，用于矢量优化

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-09-17 DOI: 10.1007/s10589-024-00609-0

Qing-Rui He, Sheng-Jie Li, Bo-Ya Zhang, Chun-Rong Chen

{"title":"A family of conjugate gradient methods with guaranteed positiveness and descent for vector optimization","authors":"Qing-Rui He, Sheng-Jie Li, Bo-Ya Zhang, Chun-Rong Chen","doi":"10.1007/s10589-024-00609-0","DOIUrl":"https://doi.org/10.1007/s10589-024-00609-0","url":null,"abstract":"In this paper, we seek a new modification way to ensure the positiveness of the conjugate parameter and, based on the Dai-Yuan (DY) method in the vector setting, propose an associated family of conjugate gradient (CG) methods with guaranteed descent for solving unconstrained vector optimization problems. Several special members of the family are analyzed and the (sufficient) descent condition is established for them (in the vector sense). Under mild conditions, a general convergence result for the CG methods with specific parameters is presented, which, in particular, covers the global convergence of the aforementioned members. Furthermore, for the purpose of comparison, we then consider the direct extension versions of some Dai-Yuan type methods which are obtained by modifying the DY method of the scalar case. These vector extensions can retrieve the classical parameters in the scalar minimization case and their descent property and global convergence are also studied under mild assumptions. Finally, numerical experiments are given to illustrate the practical behavior of all proposed methods.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142256765","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

Convergence of a quasi-Newton method for solving systems of nonlinear underdetermined equations 求解非线性欠定方程组的准牛顿法的收敛性

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-09-06 DOI: 10.1007/s10589-024-00606-3

N. Vater, A. Borzì

引用次数: 0

Scaled-PAKKT sequential optimality condition for multiobjective problems and its application to an Augmented Lagrangian method 多目标问题的 Scaled-PAKKT 顺序最优条件及其在增强拉格朗日法中的应用

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-09-02 DOI: 10.1007/s10589-024-00605-4

G. A. Carrizo, N. S. Fazzio, M. D. Sánchez, M. L. Schuverdt

引用次数: 0

A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization 基于牛顿-CG 的一般非凸圆锥优化的障碍增强拉格朗日方法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-08-30 DOI: 10.1007/s10589-024-00603-6

Chuan He, Heng Huang, Zhaosong Lu

{"title":"A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization","authors":"Chuan He, Heng Huang, Zhaosong Lu","doi":"10.1007/s10589-024-00603-6","DOIUrl":"https://doi.org/10.1007/s10589-024-00603-6","url":null,"abstract":"In this paper we consider finding an approximate second-order stationary point (SOSP) of general nonconvex conic optimization that minimizes a twice differentiable function subject to nonlinear equality constraints and also a convex conic constraint. In particular, we propose a Newton-conjugate gradient (Newton-CG) based barrier-augmented Lagrangian method for finding an approximate SOSP of this problem. Under some mild assumptions, we show that our method enjoys a total inner iteration complexity of ({widetilde{{{,mathrm{mathcal {O}},}}}}(epsilon ^{-11/2})) and an operation complexity of ({widetilde{{{,mathrm{mathcal {O}},}}}}(epsilon ^{-11/2}min {n,epsilon ^{-5/4}})) for finding an ((epsilon ,sqrt{epsilon }))-SOSP of general nonconvex conic optimization with high probability. Moreover, under a constraint qualification, these complexity bounds are improved to ({widetilde{{{,mathrm{mathcal {O}},}}}}(epsilon ^{-7/2})) and ({widetilde{{{,mathrm{mathcal {O}},}}}}(epsilon ^{-7/2}min {n,epsilon ^{-3/4}})), respectively. To the best of our knowledge, this is the first study on the complexity of finding an approximate SOSP of general nonconvex conic optimization. Preliminary numerical results are presented to demonstrate superiority of the proposed method over first-order methods in terms of solution quality.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142199604","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

Robust approximation of chance constrained optimization with polynomial perturbation 用多项式扰动对机会约束优化进行稳健逼近

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-08-28 DOI: 10.1007/s10589-024-00602-7

Bo Rao, Liu Yang, Suhan Zhong, Guangming Zhou

引用次数: 0

A power-like method for finding the spectral radius of a weakly irreducible nonnegative symmetric tensor 求弱不可还原非负对称张量谱半径的类幂方法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-08-17 DOI: 10.1007/s10589-024-00601-8

Xueli Bai, Dong-Hui Li, Lei Wu, Jiefeng Xu

引用次数: 0

An inexact regularized proximal Newton method without line search 无需直线搜索的非精确正则近似牛顿法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-08-16 DOI: 10.1007/s10589-024-00600-9

Simeon vom Dahl, Christian Kanzow

引用次数: 0

The weighted Euclidean one-center problem in $${mathbb {R}}^n$$ $${mathbb {R}}^n$ 中的加权欧几里得单中心问题

IF 1.6 2区数学

Computational Optimization and Applications Pub Date : 2024-08-08 DOI: 10.1007/s10589-024-00599-z

M. Cawood, P. Dearing

引用次数: 0

A block-coordinate approach of multi-level optimization with an application to physics-informed neural networks 应用于物理信息神经网络的多级优化块坐标方法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-08-06 DOI: 10.1007/s10589-024-00597-1

Serge Gratton, Valentin Mercier, Elisa Riccietti, Philippe L. Toint

引用次数: 0

Full-low evaluation methods for bound and linearly constrained derivative-free optimization 约束和线性约束无导数优化的全低评估方法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-08-01 DOI: 10.1007/s10589-024-00596-2

C. W. Royer, O. Sohab, L. N. Vicente

{"title":"Full-low evaluation methods for bound and linearly constrained derivative-free optimization","authors":"C. W. Royer, O. Sohab, L. N. Vicente","doi":"10.1007/s10589-024-00596-2","DOIUrl":"https://doi.org/10.1007/s10589-024-00596-2","url":null,"abstract":"Derivative-free optimization (DFO) consists in finding the best value of an objective function without relying on derivatives. To tackle such problems, one may build approximate derivatives, using for instance finite-difference estimates. One may also design algorithmic strategies that perform space exploration and seek improvement over the current point. The first type of strategy often provides good performance on smooth problems but at the expense of more function evaluations. The second type is cheaper and typically handles non-smoothness or noise in the objective better. Recently, full-low evaluation methods have been proposed as a hybrid class of DFO algorithms that combine both strategies, respectively denoted as Full-Eval and Low-Eval. In the unconstrained case, these methods showed promising numerical performance. In this paper, we extend the full-low evaluation framework to bound and linearly constrained derivative-free optimization. We derive convergence results for an instance of this framework, that combines finite-difference quasi-Newton steps with probabilistic direct-search steps. The former are projected onto the feasible set, while the latter are defined within tangent cones identified by nearby active constraints. We illustrate the practical performance of our instance on standard linearly constrained problems, that we adapt to introduce noisy evaluations as well as non-smoothness. In all cases, our method performs favorably compared to algorithms that rely solely on Full-eval or Low-eval iterations.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880890","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