D-gap functions and descent techniques for solving equilibrium problems

被引：11

作者：

Bigi, Giancarlo ^{[1
]}

Passacantando, Mauro ^{[1
]}

机构：

[1] Univ Pisa, Dipartimento Informat, I-56127 Pisa, Italy

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2015年 / 62卷 / 01期

关键词：

Equilibrium problem; D-gap function; Descent directions; Monotonicity; UNCONSTRAINED OPTIMIZATION REFORMULATIONS; VARIATIONAL INEQUALITY PROBLEMS; NEWTON METHOD; CONVERGENCE; ALGORITHM;

D O I：

10.1007/s10898-014-0223-x

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：

A new algorithm for solving equilibrium problems with differentiable bifunctions is provided. The algorithm is based on descent directions of a suitable family of D-gap functions. Its convergence is proved under assumptions which do not guarantee the equivalence between the stationary points of the D-gap functions and the solutions of the equilibrium problem. Moreover, the algorithm does not require to set parameters according to thresholds which depend on regularity properties of the equilibrium bifunction. The results of preliminary numerical tests on Nash equilibrium problems with quadratic payoffs are reported. Finally, some numerical comparisons with other D-gap algorithms are drawn relying on some further tests on linear equilibrium problems.

引用

页码：183 / 203

页数：21

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