An approximate bundle-type auxiliary problem method for solving generalized variational inequalities

Authors:
Jie Shen;Li-Ping Pang
Affiliations:
School of Mathematics, Liaoning Normal University, Dalian 116029, China;Department of Mathematics, Dalian University of Technology, Dalian 116024, China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

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Abstract

By combining the bundle idea with the auxiliary problem method we present an algorithm for solving a generalized variational inequality problem (GVIP). The proposed algorithm only requires the approximate function values and the approximate subgradients of the involved function instead of the exact ones at some points, which makes the algorithm easier to implement. In addition to that, the conditions imposed on the auxiliary functions are weaker than the preexisting results: convex is enough, not necessarily strongly convex. We also prove the weak convergence of the proposed algorithm under some conditions.