Coderivative-based semi-Newton method in nonsmooth difference programming

被引:2
作者
Aragon-Artacho, Francisco J. [1 ]
Mordukhovich, Boris S. [2 ]
Perez-Aros, Pedro [3 ]
机构
[1] Univ Alicante, Dept Math, Alicante, Spain
[2] Wayne State Univ, Dept Math, Detroit, MI 48202 USA
[3] Ctr Modelamiento Matemat CNRS, Dept Ingn Matemat, UMI 2807, Santiago, Chile
基金
美国国家科学基金会; 澳大利亚研究理事会;
关键词
Nonsmooth difference programming; Generalized Newton methods; Global convergence; Convergence rates; Variational analysis; Generalized differentiation; Classification; Nonconvex loss function; PROX-REGULARITY; TILT STABILITY; ALGORITHM;
D O I
10.1007/s10107-024-02142-8
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
This paper addresses the study of a new class of nonsmooth optimization problems, where the objective is represented as a difference of two generally nonconvex functions. We propose and develop a novel Newton-type algorithm to solving such problems, which is based on the coderivative generated second-order subdifferential (generalized Hessian) and employs advanced tools of variational analysis. Well-posedness properties of the proposed algorithm are derived under fairly general requirements, while constructive convergence rates are established by using additional assumptions including the Kurdyka-& Lstrok;ojasiewicz condition. We provide applications of the main algorithm to solving a general class of nonsmooth nonconvex problems of structured optimization that encompasses, in particular, optimization problems with explicit constraints. Finally, applications and numerical experiments are given for solving practical problems that arise in biochemical models, supervised learning, constrained quadratic programming, etc., where advantages of our algorithms are demonstrated in comparison with some known techniques and results.
引用
收藏
页数:48
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