Approximate proximal algorithms for generalized variational inequalities with paramonotonicity and pseudomonotonicity

Authors:
L. C. Ceng;T. C. Lai;J. C. Yao
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;College of Management, National Taiwan University, Taipei, Taiwan;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

We propose an approximate proximal algorithm for solving generalized variational inequalities in Hilbert space. Extension to Bregman-function-based approximate proximal algorithm is also discussed. Weak convergence of these two algorithms are established under the paramonotonicity and pseudomonotonicity assumptions of the operators.