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Computational Optimization and Applications最新文献

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Safeguarded augmented Lagrangian algorithms with scaled stopping criterion for the subproblems 对子问题采用按比例停止标准的有保障的扩增拉格朗日算法
IF 2.2 2区 数学
Computational Optimization and Applications Pub Date : 2024-04-15 DOI: 10.1007/s10589-024-00572-w
E. G. Birgin, G. Haeser, J. M. Martínez
{"title":"Safeguarded augmented Lagrangian algorithms with scaled stopping criterion for the subproblems","authors":"E. G. Birgin, G. Haeser, J. M. Martínez","doi":"10.1007/s10589-024-00572-w","DOIUrl":"https://doi.org/10.1007/s10589-024-00572-w","url":null,"abstract":"<p>At each iteration of the safeguarded augmented Lagrangian algorithm Algencan, a bound-constrained subproblem consisting of the minimization of the Powell–Hestenes–Rockafellar augmented Lagrangian function is considered, for which an approximate minimizer with tolerance tending to zero is sought. More precisely, a point that satisfies a subproblem first-order necessary optimality condition with tolerance tending to zero is required. In this work, based on the success of scaled stopping criteria in constrained optimization, we propose a scaled stopping criterion for the subproblems of Algencan. The scaling is done with the maximum absolute value of the first-order Lagrange multipliers approximation, whenever it is larger than one. The difference between the convergence theory of the scaled and non-scaled versions of Algencan is discussed and extensive numerical experiments are provided.</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578554","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
Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems 非凸多目标优化问题的 BFGS 型算法的全局收敛性
IF 2.2 2区 数学
Computational Optimization and Applications Pub Date : 2024-04-11 DOI: 10.1007/s10589-024-00571-x
L. F. Prudente, D. R. Souza
{"title":"Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems","authors":"L. F. Prudente, D. R. Souza","doi":"10.1007/s10589-024-00571-x","DOIUrl":"https://doi.org/10.1007/s10589-024-00571-x","url":null,"abstract":"<p>We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish a local superlinear rate of convergence of the method under usual conditions. Our approach employs Wolfe step sizes and ensures that the Hessian approximations are updated and corrected at each iteration to address the lack of convexity assumption. Numerical results shows that the introduced modifications preserve the practical efficiency of the BFGS method.</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578780","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
Correction: A Bregman–Kaczmarz method for nonlinear systems of equations 更正：非线性方程组的 Bregman-Kaczmarz 方法
IF 2.2 2区 数学
Computational Optimization and Applications Pub Date : 2024-04-05 DOI: 10.1007/s10589-024-00570-y
Robert Gower, Dirk A. Lorenz, Maximilian Winkler
{"title":"Correction: A Bregman–Kaczmarz method for nonlinear systems of equations","authors":"Robert Gower, Dirk A. Lorenz, Maximilian Winkler","doi":"10.1007/s10589-024-00570-y","DOIUrl":"https://doi.org/10.1007/s10589-024-00570-y","url":null,"abstract":"","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140736232","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
Nonsmooth nonconvex optimization on Riemannian manifolds via bundle trust region algorithm 通过束信任区域算法实现黎曼流形上的非光滑非凸优化
IF 2.2 2区 数学
Computational Optimization and Applications Pub Date : 2024-04-02 DOI: 10.1007/s10589-024-00569-5
N. Hoseini Monjezi, S. Nobakhtian, M. R. Pouryayevali
{"title":"Nonsmooth nonconvex optimization on Riemannian manifolds via bundle trust region algorithm","authors":"N. Hoseini Monjezi, S. Nobakhtian, M. R. Pouryayevali","doi":"10.1007/s10589-024-00569-5","DOIUrl":"https://doi.org/10.1007/s10589-024-00569-5","url":null,"abstract":"<p>This paper develops an iterative algorithm to solve nonsmooth nonconvex optimization problems on complete Riemannian manifolds. The algorithm is based on the combination of the well known trust region and bundle methods. According to the process of the most bundle methods, the objective function is approximated by a piecewise linear working model which is updated by adding cutting planes at unsuccessful trial steps. Then at each iteration, by solving a subproblem that employs the working model in the objective function subject to the trust region, a candidate descent direction is obtained. We study the algorithm from both theoretical and practical points of view and its global convergence is verified to stationary points for locally Lipschitz functions. Moreover, in order to demonstrate the reliability and efficiency, a MATLAB implementation of the proposed algorithm is prepared and results of numerical experiments are reported.</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140578618","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
SPIRAL: a superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization SPIRAL：非凸有限和最小化的超线性收敛增量近端算法
IF 2.2 2区 数学
Computational Optimization and Applications Pub Date : 2024-03-29 DOI: 10.1007/s10589-023-00550-8
Pourya Behmandpoor, Puya Latafat, Andreas Themelis, Marc Moonen, Panagiotis Patrinos
{"title":"SPIRAL: a superlinearly convergent incremental proximal algorithm for nonconvex finite sum minimization","authors":"Pourya Behmandpoor, Puya Latafat, Andreas Themelis, Marc Moonen, Panagiotis Patrinos","doi":"10.1007/s10589-023-00550-8","DOIUrl":"https://doi.org/10.1007/s10589-023-00550-8","url":null,"abstract":"<p>We introduce SPIRAL, a SuPerlinearly convergent Incremental pRoximal ALgorithm, for solving nonconvex regularized finite sum problems under a relative smoothness assumption. Each iteration of SPIRAL consists of an inner and an outer loop. It combines incremental gradient updates with a linesearch that has the remarkable property of never being triggered asymptotically, leading to superlinear convergence under mild assumptions at the limit point. Simulation results with L-BFGS directions on different convex, nonconvex, and non-Lipschitz differentiable problems show that our algorithm, as well as its adaptive variant, are competitive to the state of the art.\u0000</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140324786","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
Inexact direct-search methods for bilevel optimization problems 双层优化问题的非精确直接搜索方法
IF 2.2 2区 数学
Computational Optimization and Applications Pub Date : 2024-03-21 DOI: 10.1007/s10589-024-00567-7
Youssef Diouane, Vyacheslav Kungurtsev, Francesco Rinaldi, Damiano Zeffiro
{"title":"Inexact direct-search methods for bilevel optimization problems","authors":"Youssef Diouane, Vyacheslav Kungurtsev, Francesco Rinaldi, Damiano Zeffiro","doi":"10.1007/s10589-024-00567-7","DOIUrl":"https://doi.org/10.1007/s10589-024-00567-7","url":null,"abstract":"<p>In this work, we introduce new direct-search schemes for the solution of bilevel optimization (BO) problems. Our methods rely on a fixed accuracy blackbox oracle for the lower-level problem, and deal both with smooth and potentially nonsmooth true objectives. We thus analyze for the first time in the literature direct-search schemes in these settings, giving convergence guarantees to approximate stationary points, as well as complexity bounds in the smooth case. We also propose the first adaptation of mesh adaptive direct-search schemes for BO. Some preliminary numerical results on a standard set of bilevel optimization problems show the effectiveness of our new approaches.\u0000</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198067","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
Practical gradient and conjugate gradient methods on flag manifolds 旗流形上的实用梯度和共轭梯度方法
IF 2.2 2区 数学
Computational Optimization and Applications Pub Date : 2024-03-19 DOI: 10.1007/s10589-024-00568-6
Xiaojing Zhu, Chungen Shen
{"title":"Practical gradient and conjugate gradient methods on flag manifolds","authors":"Xiaojing Zhu, Chungen Shen","doi":"10.1007/s10589-024-00568-6","DOIUrl":"https://doi.org/10.1007/s10589-024-00568-6","url":null,"abstract":"<p>Flag manifolds, sets of nested sequences of linear subspaces with fixed dimensions, are rising in numerical analysis and statistics. The current optimization algorithms on flag manifolds are based on the exponential map and parallel transport, which are expensive to compute. In this paper we propose practical optimization methods on flag manifolds without the exponential map and parallel transport. Observing that flag manifolds have a similar homogeneous structure with Grassmann and Stiefel manifolds, we generalize some typical retractions and vector transports to flag manifolds, including the Cayley-type retraction and vector transport, the QR-based and polar-based retractions, the projection-type vector transport and the projection of the differentiated polar-based retraction as a vector transport. Theoretical properties and efficient implementations of the proposed retractions and vector transports are discussed. Then we establish Riemannian gradient and Riemannian conjugate gradient algorithms based on these retractions and vector transports. Numerical results on the problem of nonlinear eigenflags demonstrate that our algorithms have a great advantage in efficiency over the existing ones.</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140165850","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
Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: part II 非凸混合整数二次约束二次编程离散化方法的改进：第二部分
IF 2.2 2区 数学
Computational Optimization and Applications Pub Date : 2024-03-18 DOI: 10.1007/s10589-024-00554-y
Benjamin Beach, Robert Burlacu, Andreas Bärmann, Lukas Hager, Robert Hildebrand
{"title":"Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: part II","authors":"Benjamin Beach, Robert Burlacu, Andreas Bärmann, Lukas Hager, Robert Hildebrand","doi":"10.1007/s10589-024-00554-y","DOIUrl":"https://doi.org/10.1007/s10589-024-00554-y","url":null,"abstract":"<p>This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bounded and extend the well-known MIP relaxation <i>normalized multiparametric disaggregation technique</i>(NMDT), applying a sophisticated discretization to both variables. We refer to this approach as <i>doubly discretized normalized multiparametric disaggregation technique</i> (D-NMDT). In a comprehensive theoretical analysis, we underline the theoretical advantages of the enhanced method D-NMDT compared to NMDT. Furthermore, we perform a broad computational study to demonstrate its effectiveness in terms of producing tight dual bounds for MIQCQPs. Finally, we compare D-NMDT to the separable MIP relaxations from Part I and a state-of-the-art MIQCQP solver.</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140155630","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 new proximal heavy ball inexact line-search algorithm 一种新的近端重球不精确线性搜索算法
IF 2.2 2区 数学
Computational Optimization and Applications Pub Date : 2024-03-10 DOI: 10.1007/s10589-024-00565-9
S. Bonettini, M. Prato, S. Rebegoldi
{"title":"A new proximal heavy ball inexact line-search algorithm","authors":"S. Bonettini, M. Prato, S. Rebegoldi","doi":"10.1007/s10589-024-00565-9","DOIUrl":"https://doi.org/10.1007/s10589-024-00565-9","url":null,"abstract":"<p>We study a novel inertial proximal-gradient method for composite optimization. The proposed method alternates between a variable metric proximal-gradient iteration with momentum and an Armijo-like linesearch based on the sufficient decrease of a suitable merit function. The linesearch procedure allows for a major flexibility on the choice of the algorithm parameters. We prove the convergence of the iterates sequence towards a stationary point of the problem, in a Kurdyka–Łojasiewicz framework. Numerical experiments on a variety of convex and nonconvex problems highlight the superiority of our proposal with respect to several standard methods, especially when the inertial parameter is selected by mimicking the Conjugate Gradient updating rule.</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098317","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
Local convergence of primal–dual interior point methods for nonlinear semidefinite optimization using the Monteiro–Tsuchiya family of search directions 使用蒙泰罗-土屋搜索方向系列的非线性半有限优化原始双内点法的局部收敛性
IF 2.2 2区 数学
Computational Optimization and Applications Pub Date : 2024-02-28 DOI: 10.1007/s10589-024-00562-y
Takayuki Okuno
{"title":"Local convergence of primal–dual interior point methods for nonlinear semidefinite optimization using the Monteiro–Tsuchiya family of search directions","authors":"Takayuki Okuno","doi":"10.1007/s10589-024-00562-y","DOIUrl":"https://doi.org/10.1007/s10589-024-00562-y","url":null,"abstract":"<p>The recent advance of algorithms for nonlinear semidefinite optimization problems (NSDPs) is remarkable. Yamashita et al. first proposed a primal–dual interior point method (PDIPM) for solving NSDPs using the family of Monteiro–Zhang (MZ) search directions. Since then, various kinds of PDIPMs have been proposed for NSDPs, but, as far as we know, all of them are based on the MZ family. In this paper, we present a PDIPM equipped with the family of Monteiro–Tsuchiya (MT) directions, which were originally devised for solving linear semidefinite optimization problems as were the MZ family. We further prove local superlinear convergence to a Karush–Kuhn–Tucker point of the NSDP in the presence of certain general assumptions on scaling matrices, which are used in producing the MT search directions. Finally, we conduct numerical experiments to compare the efficiency among members of the MT family.\u0000</p>","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140005668","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
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