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
  • [41] THE USE OF QUADRATIC REGULARIZATION WITH A CUBIC DESCENT CONDITION FOR UNCONSTRAINED OPTIMIZATION
    Birgin, E. G.
    Martinez, J. M.
    SIAM JOURNAL ON OPTIMIZATION, 2017, 27 (02) : 1049 - 1074
  • [42] Nonconvex Homogeneous Optimization: a General Framework and Optimality Conditions of First and Second-Order
    Flores-Bazan, Fabian
    Carrillo-Galvez, Adrian
    MINIMAX THEORY AND ITS APPLICATIONS, 2024, 9 (01): : 85 - 115
  • [43] Randomized block-coordinate adaptive algorithms for nonconvex optimization problems
    Zhou, Yangfan
    Huang, Kaizhu
    Li, Jiang
    Cheng, Cheng
    Wang, Xuguang
    Hussian, Amir
    Liu, Xin
    ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE, 2023, 121
  • [44] Faster Riemannian Newton-type optimization by subsampling and cubic regularization
    Deng, Yian
    Mu, Tingting
    MACHINE LEARNING, 2023, 112 (09) : 3527 - 3589
  • [45] Faster Riemannian Newton-type optimization by subsampling and cubic regularization
    Yian Deng
    Tingting Mu
    Machine Learning, 2023, 112 : 3527 - 3589
  • [46] Proximal Gradient Algorithm with Momentum and Flexible Parameter Restart for Nonconvex Optimization
    Zhou, Yi
    Wang, Zhe
    Ji, Kaiyi
    Liang, Yingbin
    Tarokh, Vahid
    PROCEEDINGS OF THE TWENTY-NINTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE, 2020, : 1445 - 1451
  • [47] FlexPD: A Flexible Framework of First-Order Primal-Dual Algorithms for Distributed Optimization
    Mansoori, Fatemeh
    Wei, Ermin
    IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2021, 69 : 3500 - 3512
  • [48] ACCELERATED STOCHASTIC ALGORITHMS FOR NONCONVEX FINITE-SUM AND MULTIBLOCK OPTIMIZATION
    Lan, Guanghui
    Yang, Yu
    SIAM JOURNAL ON OPTIMIZATION, 2019, 29 (04) : 2753 - 2784
  • [49] Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization
    Cartis, Coralia
    Gould, Nicholas I. M.
    Toint, Philippe L.
    OPTIMIZATION METHODS & SOFTWARE, 2012, 27 (02) : 197 - 219
  • [50] Penalty Dual Decomposition Method for Nonsmooth Nonconvex Optimization-Part I: Algorithms and Convergence Analysis
    Shi, Qingjiang
    Hong, Mingyi
    IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2020, 68 : 4108 - 4122
12345