Inexact Proximal Point Algorithms and Descent Methods in Optimization

被引：0
作者：
Carlos Humes
Paulo J. S. Silva
机构：
[1] University of São Paulo,Department of Computer Science
来源：
Optimization and Engineering | 2005年 / 6卷
关键词：
proximal methods; convex programming; monotone operators;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Proximal point methods have been used by the optimization community to analyze different algorithms like multiplier methods for constrained optimization, and bundle methods for nonsmooth problems. This paper aims to be an introduction to the theory of proximal algorithms borrowing ideas from descent methods for unconstrained optimization. This new viewpoint allows us to present a simple and natural convergence proof. We also improve slightly the results from Solodov and Svaiter (1999).
引用
收藏
页码：257 / 271
页数：14
相关论文
共 50 条
  • [41] A family of conjugate gradient methods with guaranteed positiveness and descent for vector optimization
    He, Qing-Rui
    Li, Sheng-Jie
    Zhang, Bo-Ya
    Chen, Chun-Rong
    COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2024, 89 (03) : 805 - 842
  • [42] A PROXIMAL REGULARIZATION OF THE STEEPEST DESCENT METHOD
    IUSEM, AN
    SVAITER, BF
    RAIRO-RECHERCHE OPERATIONNELLE-OPERATIONS RESEARCH, 1995, 29 (02): : 123 - 130
  • [43] Proximal point algorithms involving fixed point of nonspreading-type multivalued mappings in Hilbert spaces
    Chang, Shih-Sen
    Wu, Ding Ping
    Wang, Lin
    Wang, Gang
    JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (10): : 5561 - 5569
  • [44] INEXACT PROXIMAL OPERATORS FOR lp-QUASINORM MINIMIZATION
    O'Brien, Cian
    Plumbley, Mark D.
    2018 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2018, : 4724 - 4728
  • [45] Two modified proximal point algorithms in geodesic spaces with curvature bounded above
    Kimura, Yasunori
    Kohsaka, Fumiaki
    RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2019, 68 (01) : 83 - 104
  • [46] NEW ACCURACY CRITERIA FOR MODIFIED APPROXIMATE PROXIMAL POINT ALGORITHMS IN HILBERT SPACES
    Ceng, Lu-Chuan
    Wu, Soon-Yi
    Yao, Jen-Chih
    TAIWANESE JOURNAL OF MATHEMATICS, 2008, 12 (07): : 1691 - 1705
  • [47] HYBRID PROXIMAL POINT ALGORITHMS FOR SOLVING CONSTRAINED MINIMIZATION PROBLEMS IN BANACH SPACES
    Ceng, Lu-Chuan
    Huang, Shuechin
    Liou, Yeong-Cheng
    TAIWANESE JOURNAL OF MATHEMATICS, 2009, 13 (2B): : 805 - 820
  • [48] Nonlinear rescaling and proximal-like methods in convex optimization
    Roman Polyak
    Marc Teboulle
    Mathematical Programming, 1997, 76 : 265 - 284
  • [49] Nonlinear rescaling and proximal-like methods in convex optimization
    Polyak, R
    Teboulle, M
    MATHEMATICAL PROGRAMMING, 1997, 76 (02) : 265 - 284
  • [50] The landscape of the proximal point method for nonconvex-nonconcave minimax optimization
    Grimmer, Benjamin
    Lu, Haihao
    Worah, Pratik
    Mirrokni, Vahab
    MATHEMATICAL PROGRAMMING, 2023, 201 (1-2) : 373 - 407
12345