Computational Optimization and Applications最新文献_第2页

An adaptive regularized proximal Newton-type methods for composite optimization over the Stiefel manifold 用于斯特菲尔流形上复合优化的自适应正则近端牛顿型方法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-07-26 DOI: 10.1007/s10589-024-00595-3

Qinsi Wang, Wei Hong Yang

引用次数: 0

Dynamic stochastic projection method for multistage stochastic variational inequalities 多阶段随机变分不等式的动态随机投影法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-07-26 DOI: 10.1007/s10589-024-00594-4

Bin Zhou, Jie Jiang, Hailin Sun

引用次数: 0

Extragradient method with feasible inexact projection to variational inequality problem 针对变分不等式问题的可行不精确投影外梯度法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-07-26 DOI: 10.1007/s10589-024-00592-6

R. Díaz Millán, O. P. Ferreira, J. Ugon

引用次数: 0

Handling of constraints in multiobjective blackbox optimization 多目标黑箱优化中的约束处理

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-07-16 DOI: 10.1007/s10589-024-00588-2

Jean Bigeon, Sébastien Le Digabel, Ludovic Salomon

引用次数: 0

Eigenvalue programming beyond matrices 超越矩阵的特征值编程

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-07-10 DOI: 10.1007/s10589-024-00591-7

Masaru Ito, Bruno F. Lourenço

{"title":"Eigenvalue programming beyond matrices","authors":"Masaru Ito, Bruno F. Lourenço","doi":"10.1007/s10589-024-00591-7","DOIUrl":"https://doi.org/10.1007/s10589-024-00591-7","url":null,"abstract":"In this paper we analyze and solve eigenvalue programs, which consist of the task of minimizing a function subject to constraints on the “eigenvalues” of the decision variable. Here, by making use of the FTvN systems framework introduced by Gowda, we interpret “eigenvalues” in a broad fashion going beyond the usual eigenvalues of matrices. This allows us to shed new light on classical problems such as inverse eigenvalue problems and also leads to new applications. In particular, after analyzing and developing a simple projected gradient algorithm for general eigenvalue programs, we show that eigenvalue programs can be used to express what we call vanishing quadratic constraints. A vanishing quadratic constraint requires that a given system of convex quadratic inequalities be satisfied and at least a certain number of those inequalities must be tight. As a particular case, this includes the problem of finding a point x in the intersection of m ellipsoids in such a way that x is also in the boundary of at least (ell ) of the ellipsoids, for some fixed (ell > 0). At the end, we also present some numerical experiments.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587285","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

Q-fully quadratic modeling and its application in a random subspace derivative-free method 全二次方建模及其在随机子空间无导数方法中的应用

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-06-20 DOI: 10.1007/s10589-024-00590-8

Yiwen Chen, Warren Hare, Amy Wiebe

{"title":"Q-fully quadratic modeling and its application in a random subspace derivative-free method","authors":"Yiwen Chen, Warren Hare, Amy Wiebe","doi":"10.1007/s10589-024-00590-8","DOIUrl":"https://doi.org/10.1007/s10589-024-00590-8","url":null,"abstract":"Model-based derivative-free optimization (DFO) methods are an important class of DFO methods that are known to struggle with solving high-dimensional optimization problems. Recent research has shown that incorporating random subspaces into model-based DFO methods has the potential to improve their performance on high-dimensional problems. However, most of the current theoretical and practical results are based on linear approximation models due to the complexity of quadratic approximation models. This paper proposes a random subspace trust-region algorithm based on quadratic approximations. Unlike most of its precursors, this algorithm does not require any special form of objective function. We study the geometry of sample sets, the error bounds for approximations, and the quality of subspaces. In particular, we provide a technique to construct Q-fully quadratic models, which is easy to analyze and implement. We present an almost-sure global convergence result of our algorithm and give an upper bound on the expected number of iterations to find a sufficiently small gradient. We also develop numerical experiments to compare the performance of our algorithm using both linear and quadratic approximation models. The numerical results demonstrate the strengths and weaknesses of using quadratic approximations.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505104","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 nonsmooth primal-dual method with interwoven PDE constraint solver 带有交织 PDE 约束求解器的非平滑原始二元法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-06-08 DOI: 10.1007/s10589-024-00587-3

Bjørn Jensen, Tuomo Valkonen

引用次数: 0

Stochastic Steffensen method 随机斯蒂芬森法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-06-07 DOI: 10.1007/s10589-024-00583-7

Minda Zhao, Zehua Lai, Lek-Heng Lim

{"title":"Stochastic Steffensen method","authors":"Minda Zhao, Zehua Lai, Lek-Heng Lim","doi":"10.1007/s10589-024-00583-7","DOIUrl":"https://doi.org/10.1007/s10589-024-00583-7","url":null,"abstract":"Is it possible for a first-order method, i.e., only first derivatives allowed, to be quadratically convergent? For univariate loss functions, the answer is yes—the Steffensen method avoids second derivatives and is still quadratically convergent like Newton method. By incorporating a specific step size we can even push its convergence order beyond quadratic to (1+sqrt{2} approx 2.414). While such high convergence orders are a pointless overkill for a deterministic algorithm, they become rewarding when the algorithm is randomized for problems of massive sizes, as randomization invariably compromises convergence speed. We will introduce two adaptive learning rates inspired by the Steffensen method, intended for use in a stochastic optimization setting and requires no hyperparameter tuning aside from batch size. Extensive experiments show that they compare favorably with several existing first-order methods. When restricted to a quadratic objective, our stochastic Steffensen methods reduce to randomized Kaczmarz method—note that this is not true for SGD or SLBFGS—and thus we may also view our methods as a generalization of randomized Kaczmarz to arbitrary objectives.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548136","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

Polynomial worst-case iteration complexity of quasi-Newton primal-dual interior point algorithms for linear programming 线性规划准牛顿原始双内点算法的多项式最坏迭代复杂度

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-06-07 DOI: 10.1007/s10589-024-00584-6

Jacek Gondzio, Francisco N. C. Sobral

{"title":"Polynomial worst-case iteration complexity of quasi-Newton primal-dual interior point algorithms for linear programming","authors":"Jacek Gondzio, Francisco N. C. Sobral","doi":"10.1007/s10589-024-00584-6","DOIUrl":"https://doi.org/10.1007/s10589-024-00584-6","url":null,"abstract":"Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization problems or the Jacobian in system of nonlinear equations. In the Interior Point context, quasi-Newton algorithms compute low-rank updates of the matrix associated with the Newton systems, instead of computing it from scratch at every iteration. In this work, we show that a simplified quasi-Newton primal-dual interior point algorithm for linear programming, which alternates between Newton and quasi-Newton iterations, enjoys polynomial worst-case iteration complexity. Feasible and infeasible cases of the algorithm are considered and the most common neighborhoods of the central path are analyzed. To the best of our knowledge, this is the first attempt to deliver polynomial worst-case iteration complexity bounds for these methods. Unsurprisingly, the worst-case complexity results obtained when quasi-Newton directions are used are worse than their counterparts when Newton directions are employed. However, quasi-Newton updates are very attractive for large-scale optimization problems where the cost of factorizing the matrices is much higher than the cost of solving linear systems.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548135","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

Projection free methods on product domains 乘积域上的无投影方法

IF 2.2 2区数学

Computational Optimization and Applications Pub Date : 2024-06-04 DOI: 10.1007/s10589-024-00585-5

Immanuel Bomze, Francesco Rinaldi, Damiano Zeffiro

引用次数: 0