TY - JOUR
T1 - Weakly sharp solutions and finite convergence of algorithms for a variational inequality problem
AU - Liu, Yina
N1 - Publisher Copyright:
© 2017 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2018/2/1
Y1 - 2018/2/1
N2 - The aim of the paper is to characterize weakly sharp solutions of a variational inequality problem. In particular, we present weak sharpness results by using primal and dual gap functions, g and G, and also without considering gap functions, either. The subdifferential and locally Lipschitz properties of g + λG for λ > 0 are first studied since they are useful for discussing weakly sharp solutions of the variational inequality. A result of finite termination of a class of algorithms for solving the variational inequality problem is also studied.
AB - The aim of the paper is to characterize weakly sharp solutions of a variational inequality problem. In particular, we present weak sharpness results by using primal and dual gap functions, g and G, and also without considering gap functions, either. The subdifferential and locally Lipschitz properties of g + λG for λ > 0 are first studied since they are useful for discussing weakly sharp solutions of the variational inequality. A result of finite termination of a class of algorithms for solving the variational inequality problem is also studied.
KW - Variational inequality
KW - convergence of an algorithm
KW - error bound
KW - gap functions
KW - gâteaux differentiable
KW - locally Lipschitz property
KW - weakly sharp solution
UR - http://www.scopus.com/inward/record.url?scp=85032834894&partnerID=8YFLogxK
U2 - 10.1080/02331934.2017.1397146
DO - 10.1080/02331934.2017.1397146
M3 - Article
AN - SCOPUS:85032834894
SN - 0233-1934
VL - 67
SP - 329
EP - 340
JO - Optimization
JF - Optimization
IS - 2
ER -