WANG Li-Na , LI Ming-Hua . Error bounds of regularized gap functions for smooth and nonmonotone variational inequality problems[J]. Journal of East China Normal University(Natural Science), 2015 , 2015(1) : 61 -67 . DOI: 10.3969/j.issn.1000-5641.2015.01.007

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.