华东师范大学学报（自然科学版） >

2015 , Vol. 2015 >Issue 1: 61 - 67

DOI: https://doi.org/10.3969/j.issn.1000-5641.2015.01.007

应用数学与基础数学

光滑非单调变分不等式问题正则间隙函数的误差界(英)

  • 王丽娜 ,
  • 李明华
展开
  • 1. 重庆水利电力职业技术学院 重庆 402160; 2. 西北农林科技大学~~理学院 陕西 712100

收稿日期: 2014-01-01

  网络出版日期: 2015-03-29

基金资助

西北农林科技大学博士科研启动经费及陕西省专项配套经费(Z111021301)

重庆水利电力职业技术学院院级科研项目(K201319)

 

收起

Error bounds of regularized gap functions for smooth and nonmonotone variational inequality problems

  • WANG Li-Na ,
  • LI Ming-Hua
Expand

Received date: 2014-01-01

  Online published: 2015-03-29

Supported by

null

Fold

摘要

在不同的条件下, 利用一类正则间隙函数,建立非单调变分不等式问题的两类全局误差界

关键词： 误差界; 正则间隙函数; 变分不等式

本文引用格式

王丽娜 , 李明华 . 光滑非单调变分不等式问题正则间隙函数的误差界(英)[J]. 华东师范大学学报（自然科学版）, 2015 , 2015(1) : 61 -67 . DOI: 10.3969/j.issn.1000-5641.2015.01.007

Abstract

By using a class of regularized gap functions for a variational inequality problem, two kinds of global error bounds of the nonmonotone variational inequality problem under some different conditions was established.

Key words： error bound; regularized gap function; variational inequality problem

参考文献

FACCHINEI F, PANG J S. Finite-Dimensional Variational Inequalities and Complementarity Problems [M]. Berlin: Springer, 2003.
AUCHMUTY G. Variational principles for variational inequalities [J]. Numer Funct Anal Optim, 1989(10): 863-874.
AUSLENDER A. Optimization: M\'{e}thodes Numériques [M]. Paris, France: Masson, 1976.
FUKUSHIMA M. Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems [J]. Math Program, 1992, 53: 99-110.
HARKER P T, PANG J S. Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications [J]. Math Program, 1990, 48: 161-220.
HUANG L R, NG K F. Equivalent optimization formulations and error bounds for variational inequality problems [J]. J Optim Theory Appl, 2005, 125: 299-314.
NG K F, TAN L L.Error bounds of regularized gap functions for nonsmooth variational inequality problems [J]. Math Program, 2007, 110: 405-429.
WU J H, FLORIAN M, MARCOTTE P. A general descent framework for the monotone variational inequality problem [J]. Math Program, 1993, 61: 281-300.
YAMASHITA N, TAJI K, FUKUSHIMA M. Unconstrained optimization reformulations of variational inequality problems [J]. J Optim Theory Appl, 1997, 92: 439-456.
PENG J M. Equivalence of variational inequality problems to unconstrained optimization [J]. Math Program, 1997, 78: 347-355.
LI G, NG K F. Error bounds of generalized D-gap functions for nonsmooth and nonmonotone variational inequality problems [J]. SIAM J Optim, 2009. 20: 667-690.
QU B, WANG C Y, ZHANG J Z. Convergence and error bound of a method for solving variational inequality problems via the generalized D-gap function [J]. J Optim Theory Appl, 2003, 119: 535-552.
YAMASHITA N, FUKUSHIMA M. Equivalent unconstrained minimization and global error bounds for variational inequality problems [J]. SIAM J Control Optim, 1997, 35: 273-284.
LI G, TANG C, WEI Z. Error bound results for generalized D-gap functions of nonsmooth variational inequality problems [J]. J Comput Appl Math, 2010, 233: 2795-2806.
NG K F, ZHENG X Y. Error Bounds for lower semicontinuous functions in normed spaces [J]. SIAM J Optim, 2001, 12: 1-17.
Options
文章导航

/

〈 〉