A multi-step doubly stabilized bundle method for nonsmooth convex optimization

被引：3
|
作者：
Tang, Chunming [1 ]
Liu, Shuai [2 ]
Jian, Jinbao [3 ]
Ou, Xiaomei [1 ]
机构：
[1] Guangxi Univ, Coll Math & Informat Sci, Nanning 530004, Peoples R China
[2] South China Normal Univ, Sch Software, Nanhai Campus, Foshan 528225, Peoples R China
[3] Guangxi Univ Nationalities, Sch Math & Informat Sci, Nanning 530006, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 376卷
基金：
中国国家自然科学基金;
关键词：
Nonsmooth optimization; Doubly stabilized bundle method; Multi-step scheme; Descent test criterion; Global convergence; DIRECTION METHOD; VERSION;
D O I：
10.1016/j.amc.2020.125154
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, by incorporating a multi-step scheme into the doubly stabilized bundle method (DSBM) recently developed by Oliveira and Solodov (2016), we propose a multistep doubly stabilized bundle method (MDSBM) for solving nonsmooth convex optimization problems. In contrast to a single sequence generated by DSBM, the MDSBM generates three related iteration sequences. One is used to build the cutting-planes model of the objective function, another is served as the stability centers, and the third is the sequence of solutions to our new doubly stabilized subproblems. In addition, we present a new descent test criterion, aiming to take advantage of the multi-step scheme. We establish global convergence of the proposed method, and finally present some promising numerical results. (C) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页数：16
相关论文
共 50 条
  • [41] A Multi-Step Sequential System Optimization Design Method for Upper Stages
    Bohlouri, Vahid
    Zakeri, Mostafa
    Nosratollahi, Mehran
    [J]. JOURNAL OF AEROSPACE TECHNOLOGY AND MANAGEMENT, 2023, 15
  • [42] A variable metric method for nonsmooth convex constrained optimization
    Peng, Yehui
    Liu, Zhenhai
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 183 (02) : 961 - 971
  • [43] A SELF-ADAPTIVE ALGORITHM WITH MULTI-STEP INERTIA FOR SOLVING CONVEX BILEVEL OPTIMIZATION PROBLEMS
    Duan, Peichao
    Li, Huan
    [J]. Journal of Applied and Numerical Optimization, 2024, 6 (03): : 447 - 460
  • [44] Globally convergent BFGS method for nonsmooth convex optimization
    Rauf, AI
    Fukushima, M
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2000, 104 (03) : 539 - 558
  • [45] High-dimensional sparse index tracking based on a multi-step convex optimization approach
    Shi, Fangquan
    Shu, Lianjie
    Luo, Yiling
    Huo, Xiaoming
    [J]. QUANTITATIVE FINANCE, 2023, 23 (09) : 1361 - 1372
  • [46] A multi-step method for speaker identification
    Savastano, M.
    Luciano, A.
    Pagano, A.
    Peticone, B.
    Riccardi, L.
    [J]. 2006 IEEE INFORMATION ASSURANCE WORKSHOP, 2006, : 393 - +
  • [47] Multi-Step Gradient Methods for Networked Optimization
    Ghadimi, Euhanna
    Shames, Iman
    Johansson, Mikael
    [J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2013, 61 (21) : 5417 - 5429
  • [48] Illumination system design with multi-step optimization
    Magarill, Simon
    Cassarly, William J.
    [J]. NONIMAGING OPTICS: EFFICIENT DESIGN FOR ILLUMINATION AND SOLAR CONCENTRATION XII, 2015, 9572
  • [49] Subspace identification as multi-step predictions optimization
    Trnka, P
    Havlena, V
    [J]. PROCEEDINGS OF THE FIFTH IASTED INTERNATIONAL CONFERENCE ON MODELLING, SIMULATION, AND OPTIMIZATION, 2005, : 223 - 228
  • [50] Multi-Step Skipping Methods for Unconstrained Optimization
    Ford, John A.
    Aamir, Nudrat
    [J]. NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS A-C, 2011, 1389
12345