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

[21] 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
[22] On generic locally convex vector functions
Gershkovich, V
Craven, BD
Ralph, D
PROGRESS IN OPTIMIZATION: CONTRIBUTIONS FROM AUSTRALASIA, 2000, 39 : 135 - 152
[23] On Faster Convergence of Cyclic Block Coordinate Descent-type Methods for Strongly Convex Minimization
Li, Xingguo
Zhao, Tuo
Arora, Raman
Liu, Han
Hong, Mingyi
JOURNAL OF MACHINE LEARNING RESEARCH, 2018, 18
[24] ONE CLASS OF METHODS OF UNCONDITIONAL MINIMIZATION OF A CONVEX FUNCTION, HAVING A HIGH-RATE OF CONVERGENCE
NESTEROV, YE
USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1984, 24 (04): : 80 - 82
[25] On a combination of convex risk minimization methods
Christmann, A
Classification - the Ubiquitous Challenge, 2005, : 434 - 441
[26] OPTIMAL METHODS OF SMOOTH CONVEX MINIMIZATION
NEMIROVSKII, AS
NESTEROV, YE
USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1985, 25 (02): : 21 - 30
[27] Linear convergence of epsilon-subgradient descent methods for a class of convex functions
Robinson, SM
MATHEMATICAL PROGRAMMING, 1999, 86 (01) : 41 - 50
[28] CONVERGENCE OF A RANDOM SEARCH METHOD IN CONVEX MINIMIZATION PROBLEMS
KARMANOV, VG
TEORIYA VEROYATNOSTEI I YEYE PRIMENIYA, 1974, 19 (04): : 817 - 824
[29] Convergence of the Gradient Projection Method for Generalized Convex Minimization
Changyu Wang
Naihua Xiu
Computational Optimization and Applications, 2000, 16 : 111 - 120
[30] Convergence of the gradient projection method for generalized convex minimization
Wang, CY
Xiu, NH
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2000, 16 (02) : 111 - 120

← 1 2 3 4 5 →