NEW VARIANTS OF BUNDLE METHODS

被引:249
作者
LEMARECHAL, C [1 ]
NEMIROVSKII, A [1 ]
NESTEROV, Y [1 ]
机构
[1] CENT ECON & MATH INST,MOSCOW 117481,RUSSIA
关键词
NONSMOOTH CONVEX OPTIMIZATION; BUNDLE METHODS;
D O I
10.1007/BF01585555
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
In this paper we describe a number of new variants of bundle methods for nonsmooth unconstrained and constrained convex optimization, convex-concave games and variational inequalities. We outline the ideas underlying these methods and present rate-of-convergence estimates.
引用
收藏
页码:111 / 147
页数:37
相关论文
共 21 条
[1]  
AUSLENDER A, 1972, LECTURE NOTES EC MAT
[2]  
Cheney E.W., 1959, NUMER MATH, V1, P253
[3]  
ERMOLIEV YM, 1966, CYBERNETICS, V4, P1
[4]  
Held M, 1971, MATHEMATICAL PROGRAM, V1, P6, DOI [DOI 10.1007/BF01584070, 10.1007/BF01584070]
[5]  
HUARD P, 1967, NONLINEAR PROGRAMMIN, P206
[6]   THE CUTTING-PLANE METHOD FOR SOLVING CONVEX PROGRAMS [J].
KELLEY, JE .
JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1960, 8 (04) :703-712
[7]   PROXIMITY CONTROL IN BUNDLE METHODS FOR CONVEX NONDIFFERENTIABLE MINIMIZATION [J].
KIWIEL, KC .
MATHEMATICAL PROGRAMMING, 1990, 46 (01) :105-122
[8]   AN AGGREGATE SUBGRADIENT METHOD FOR NONSMOOTH CONVEX MINIMIZATION [J].
KIWIEL, KC .
MATHEMATICAL PROGRAMMING, 1983, 27 (03) :320-341
[9]  
LEBEDEV VY, 1977, J NUMERICAL MATH MAT, V12, P765
[10]  
LEMAR\ECHAL C., 1975, NONDIFFERENTIABLE OP, P95