ON THE GLOBAL OPTIMIZATION PROPERTIES OF FINITE-DIFFERENCE LOCAL DESCENT ALGORITHMS

被引:11
作者
ZAVRIEV, SK [1 ]
机构
[1] MOSCOW MV LOMONOSOV STATE UNIV,FAC COMPUTAT MATH & CYBERNET,MOSCOW 119899,RUSSIA
关键词
GRADIENT METHOD; COORDINATE DESCENT METHOD; GLOBAL OPTIMIZATION; STABILITY UNDER PERTURBATIONS;
D O I
10.1007/BF01100240
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
The paper is devoted to the convergence properties of finite-difference local descent algorithms in global optimization problems with a special gamma-convex structure. It is assumed that the objective function can be closely approximated by some smooth convex function. Stability properties of the perturbed gradient descent and coordinate descent methods are investigated. Basing on this results some global optimization properties of finite-difference local descent algorithms, in particular, coordinate descent method, are discovered. These properties are not inherent in methods using exact gradients.
引用
收藏
页码:67 / 78
页数:12
相关论文
共 12 条
[1]  
[Anonymous], 2016, LINEAR NONLINEAR PRO
[2]  
BOGGS PT, 1976, MATH COMPUT, V30, P199, DOI 10.1090/S0025-5718-1976-0395209-4
[3]  
DOROFEYEV PA, 1985, ZH VYCHISL MAT MAT F, V25, P181
[4]  
EVTUSHENKO UG, 1971, USSR COMP MATH MATH, V11, P1390
[6]   OPTIMIZATION OF GLOBALLY CONVEX-FUNCTIONS [J].
HU, TC ;
KLEE, V ;
LARMAN, D .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1989, 27 (05) :1026-1047
[7]   NONDIFFERENTIAL OPTIMIZATION VIA ADAPTIVE SMOOTHING [J].
MAYNE, DQ ;
POLAK, E .
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1984, 43 (04) :601-613
[8]  
MIKHALEVITCH VS, 1987, METHODS NONCONVEX OP
[9]  
NORKIN VI, 1979, KIBERNETICA, V6, P73
[10]  
Polyak BT., 1987, INTRO OPTIMIZATION, V1