Computational Optimization and Applications最新文献

Distributed inexact Newton method with adaptive step sizes. 具有自适应步长的分布不精确牛顿法。

IF 1.6 2区数学

Computational Optimization and Applications Pub Date : 2025-01-01 Epub Date: 2025-02-26 DOI: 10.1007/s10589-025-00666-z

Dušan Jakovetić, Nataša Krejić, Greta Malaspina

{"title":"Distributed inexact Newton method with adaptive step sizes.","authors":"Dušan Jakovetić, Nataša Krejić, Greta Malaspina","doi":"10.1007/s10589-025-00666-z","DOIUrl":"10.1007/s10589-025-00666-z","url":null,"abstract":"We consider two formulations for distributed optimization wherein N nodes in a generic connected network solve a problem of common interest: distributed personalized optimization and consensus optimization. A new method termed DINAS (Distributed Inexact Newton method with Adaptive step size) is proposed. DINAS employs large adaptively computed step sizes, requires a reduced global parameters knowledge with respect to existing alternatives, and can operate without any local Hessian inverse calculations nor Hessian communications. When solving personalized distributed learning formulations, DINAS achieves quadratic convergence with respect to computational cost and linear convergence with respect to communication cost, the latter rate being independent of the local functions condition numbers or of the network topology. When solving consensus optimization problems, DINAS is shown to converge to the global solution. Extensive numerical experiments demonstrate significant improvements of DINAS over existing alternatives. As a result of independent interest, we provide for the first time convergence analysis of the Newton method with the adaptive Polyak's step size when the Newton direction is computed inexactly in centralized environment.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":"91 2","pages":"683-715"},"PeriodicalIF":1.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12085390/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144103095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Off-the-grid regularisation for Poisson inverse problems. 泊松反问题的离网正则化。

IF 1.6 2区数学

Computational Optimization and Applications Pub Date : 2025-01-01 Epub Date: 2025-05-04 DOI: 10.1007/s10589-025-00688-7

Marta Lazzaretti, Claudio Estatico, Alejandro Melero, Luca Calatroni

{"title":"Off-the-grid regularisation for Poisson inverse problems.","authors":"Marta Lazzaretti, Claudio Estatico, Alejandro Melero, Luca Calatroni","doi":"10.1007/s10589-025-00688-7","DOIUrl":"10.1007/s10589-025-00688-7","url":null,"abstract":"Off-the-grid regularisation has been extensively employed over the last decade in the context of ill-posed inverse problems formulated in the continuous setting of the space of Radon measures <math><mrow><mi>M</mi> <mo>(</mo> <mi>Ω</mi> <mo>)</mo></mrow> </math> . These approaches enjoy convexity and counteract the discretisation biases as well the numerical instabilities typical of their discrete counterparts. In the framework of sparse reconstruction of discrete point measures (sum of weighted Diracs), a Total Variation regularisation norm in <math><mrow><mi>M</mi> <mo>(</mo> <mi>Ω</mi> <mo>)</mo></mrow> </math> is typically combined with an <math><msup><mi>L</mi> <mn>2</mn></msup> </math> data term modelling additive Gaussian noise. To assess the framework of off-the-grid regularisation in the presence of signal-dependent Poisson noise, we consider in this work a variational model where Total Variation regularisation is coupled with a Kullback-Leibler data term under a non-negativity constraint. Analytically, we study the optimality conditions of the composite functional and analyse its dual problem. Then, we consider an homotopy strategy to select an optimal regularisation parameter and use it within a Sliding Frank-Wolfe algorithm. Several numerical experiments on both 1D/2D/3D simulated and real 3D fluorescent microscopy data are reported.","PeriodicalId":55227,"journal":{"name":"Computational Optimization and Applications","volume":"91 2","pages":"827-860"},"PeriodicalIF":1.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12085367/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144103167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

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":"47 1","pages":""},"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":"165 1","pages":""},"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

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