A Flexible Framework for Cubic Regularization Algorithms for Nonconvex Optimization in Function Space

被引：1
|
作者：
Schiela, Anton [1 ]
机构：
[1] Univ Bayreuth, Math Inst, D-95440 Bayreuth, Germany
来源：
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2019年 / 40卷 / 01期
关键词：
Non-convex optimization; optimization in function space; cubic regularization; GLOBAL CONVERGENCE; TRUST; MINIMIZATION;
D O I：
10.1080/01630563.2018.1499114
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and local convergence results are established in a general framework.
引用
收藏
页码：85 / 118
页数：34
相关论文
共 50 条
  • [31] A hybrid stochastic optimization framework for composite nonconvex optimization
    Quoc Tran-Dinh
    Nhan H. Pham
    Dzung T. Phan
    Lam M. Nguyen
    Mathematical Programming, 2022, 191 : 1005 - 1071
  • [32] Nonconvex Sparse Regularization and Convex Optimization for Bearing Fault Diagnosis
    Wang, Shibin
    Selesnick, Ivan
    Cai, Gaigai
    Feng, Yining
    Sui, Xin
    Chen, Xuefeng
    IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 2018, 65 (09) : 7332 - 7342
  • [33] A function space framework for structural total variation regularization with applications in inverse problems
    Hintermuller, Michael
    Holler, Martin
    Papafitsoros, Kostas
    INVERSE PROBLEMS, 2018, 34 (06)
  • [34] AdaCN: An Adaptive Cubic Newton Method for Nonconvex Stochastic Optimization
    Liu, Yan
    Zhang, Maojun
    Zhong, Zhiwei
    Zeng, Xiangrong
    COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE, 2021, 2021
  • [35] IMPROVEMENT AND IMPLEMENTATION OF SOME ALGORITHMS FOR NONCONVEX OPTIMIZATION PROBLEMS
    THIEU, TV
    LECTURE NOTES IN MATHEMATICS, 1989, 1405 : 159 - 170
  • [36] An Improved SAR Imaging Method Based on Nonconvex Regularization and Convex Optimization
    Wei, Zhonghao
    Zhang, Bingchen
    Xu, Zhilin
    Han, Bing
    Hong, Wen
    Wu, Yirong
    IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, 2019, 16 (10) : 1580 - 1584
  • [37] Bregman iterative regularization using model functions for nonconvex nonsmooth optimization
    Yang, Haoxing
    Zhang, Hui
    Wang, Hongxia
    Cheng, Lizhi
    FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS, 2022, 8
  • [38] Regional complexity analysis of algorithms for nonconvex smooth optimization
    Frank E. Curtis
    Daniel P. Robinson
    Mathematical Programming, 2021, 187 : 579 - 615
  • [39] Regional complexity analysis of algorithms for nonconvex smooth optimization
    Curtis, Frank E.
    Robinson, Daniel P.
    MATHEMATICAL PROGRAMMING, 2021, 187 (1-2) : 579 - 615
  • [40] Nonconvex Optimization in Mechanics: Algorithms, Heuristics and Engineering Applications
    E.S. Mistakidis
    G.E. Stavroulakis
    Meccanica, 1999, 34 (4) : 300 - 301
12345