Generic convergence of minimization methods for convex functions

被引：0

作者：

Reich, S ^{[1
]}

Zaslavski, AJ ^{[1
]}

机构：

[1] Technion Israel Inst Technol, Dept Mat Sci, IL-32000 Haifa, Israel

来源：

FIXED POINT THEORY AND APPLICATIONS, VOL 2 | 2001年

关键词：

complete metric space; convex function; descent method; generic property; Lipschitzian function; Lyapunov function; potosity;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This is a survey of recent results regarding the convergence of several classes of algorithms for the minimization of convex functions defined on a general Banach space. For each class, we define an appropriate complete metric space of algorithms and show that most of them (in the sense of Baire's categories) are convergent. In some cases the set of divergent methods is not only of the first category, but also a-porous.

引用

页码：73 / 88

页数：16

共 50 条

[1] Generic convergence of descent methods in Banach spaces
Reich, S
Zaslavski, AJ
MATHEMATICS OF OPERATIONS RESEARCH, 2000, 25 (02) : 231 - 242
[2] STRONGLY CONVEX FUNCTIONS, MOREAU ENVELOPES, AND THE GENERIC NATURE OF CONVEX FUNCTIONS WITH STRONG MINIMIZERS
Planiden, C.
Wang, X.
SIAM JOURNAL ON OPTIMIZATION, 2016, 26 (02) : 1341 - 1364
[3] Inexact descent methods for convex minimization problems in Banach spaces
Reich, Simeon
Zaslavski, Alexander J.
CARPATHIAN JOURNAL OF MATHEMATICS, 2020, 36 (01) : 141 - 146
[4] A generic convergence theorem for continuous descent methods in Banach spaces
Aizicovici, Sergiu
Reich, Simeon
Zaslavski, Alexander J.
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2007, 14 (01): : 137 - 145
[5] On the Redundancy of Hessian Nonsingularity for Linear Convergence Rate of the Newton Method Applied to the Minimization of Convex Functions
Evtushenko, Yu. G.
Tret'yakov, A. A.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2024, 64 (04) : 781 - 787
[6] INEXACT DESCENT METHODS WITH CONVEX OBJECTIVE FUNCTIONS IN BANACH SPACES
Reich, Simeon
Zaslavski, Alexander J.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2019, 20 (09) : 1875 - 1882
[7] MINIMIZING CONVEX FUNCTIONS BY CONTINUOUS DESCENT METHODS
Aizicovici, Sergiu
Reich, Simeon
Zaslavski, Alexander J.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2010,
[8] LIPSCHITZ REGULARIZATION AND THE CONVERGENCE OF CONVEX-FUNCTIONS
BEER, G
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1994, 15 (1-2) : 31 - 46
[9] On generic convergence of successive approximations of mappings with convex and compact point images
Bargetz, Christian
Medjic, Emir
Pirk, Katriin
MONATSHEFTE FUR MATHEMATIK, 2022, 202 (4): : 659 - 683
[10] On generic convergence of successive approximations of mappings with convex and compact point images
Christian Bargetz
Emir Medjic
Katriin Pirk
Monatshefte für Mathematik, 2023, 202 : 659 - 683

← 1 2 3 4 5 →