A splitting bundle approach for non-smooth non-convex minimization

被引：15
|
作者：
Fuduli, A. [1 ]
Gaudioso, M. [2 ]
Nurminski, E. A. [3 ,4 ]
机构：
[1] Univ Calabria, Dipartimento Matemat & Informat, I-87036 Arcavacata Di Rende, Italy
[2] Univ Calabria, Dipartimento Ingn Informat Modellist Elettron & S, I-87036 Arcavacata Di Rende, Italy
[3] Far Eastern Fed Univ, Vladivostok, Russia
[4] Inst Automat & Control Problems Far Eastern Branc, Vladivostok, Russia
来源：
OPTIMIZATION | 2015年 / 64卷 / 05期
关键词：
90C26; 65K05; bundle methods; non-convex optimization; non-smooth optimization; GRADIENT SAMPLING ALGORITHM; CONVEX MINIMIZATION; PROXIMITY CONTROL; OPTIMIZATION; CONVERGENCE; CLASSIFICATION; APPROXIMATIONS; STRATEGY; PROGRAMS;
D O I：
10.1080/02331934.2013.840625
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
We present a bundle-type method for minimizing non-convex non-smooth functions. Our approach is based on the partition of the bundle into two sets, taking into account the local convex or concave behaviour of the objective function. Termination at a point satisfying an approximate stationarity condition is proved and numerical results are provided. © 2013 Taylor & Francis.
引用
收藏
页码：1131 / 1151
页数：21
相关论文
共 50 条
  • [1] Minimization of Non-smooth, Non-convex Functionals by Iterative Thresholding
    Bredies, Kristian
    Lorenz, Dirk A.
    Reiterer, Stefan
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2015, 165 (01) : 78 - 112
  • [2] Minimization of Non-smooth, Non-convex Functionals by Iterative Thresholding
    Kristian Bredies
    Dirk A. Lorenz
    Stefan Reiterer
    [J]. Journal of Optimization Theory and Applications, 2015, 165 : 78 - 112
  • [3] A BUNDLE TYPE APPROACH TO THE UNCONSTRAINED MINIMIZATION OF CONVEX NON-SMOOTH FUNCTIONS
    GAUDIOSO, M
    MONACO, MF
    [J]. MATHEMATICAL PROGRAMMING, 1982, 23 (02) : 216 - 226
  • [4] Non-smooth Non-convex Bregman Minimization: Unification and New Algorithms
    Peter Ochs
    Jalal Fadili
    Thomas Brox
    [J]. Journal of Optimization Theory and Applications, 2019, 181 : 244 - 278
  • [5] Non-smooth Non-convex Bregman Minimization: Unification and New Algorithms
    Ochs, Peter
    Fadili, Jalal
    Brox, Thomas
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2019, 181 (01) : 244 - 278
  • [6] Relaxed Majorization-Minimization for Non-Smooth and Non-Convex Optimization
    Xu, Chen
    Lin, Zhouchen
    Zhao, Zhenyu
    Zha, Hongbin
    [J]. THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE, 2016, : 812 - 818
  • [7] Nested Alternating Minimization with FISTA for Non-convex and Non-smooth Optimization Problems
    Gur, Eyal
    Sabach, Shoham
    Shtern, Shimrit
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2023, 199 (03) : 1130 - 1157
  • [8] Nested Alternating Minimization with FISTA for Non-convex and Non-smooth Optimization Problems
    Eyal Gur
    Shoham Sabach
    Shimrit Shtern
    [J]. Journal of Optimization Theory and Applications, 2023, 199 : 1130 - 1157
  • [9] Reduced subgradient bundle method for linearly constrained non-smooth non-convex problems
    El Ghali, A.
    El Moudden, M.
    [J]. OPTIMIZATION, 2021, 70 (10) : 2103 - 2130
  • [10] Primal–Dual Proximal Splitting and Generalized Conjugation in Non-smooth Non-convex Optimization
    Christian Clason
    Stanislav Mazurenko
    Tuomo Valkonen
    [J]. Applied Mathematics & Optimization, 2021, 84 : 1239 - 1284
12345