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A Relative Error Tolerance for a Family of Generalized Proximal Point Methods

Engenharia de Sistemas e Computação, COPPE-UFRJ, CP 68511, Rio de Janeiro-RJ, CEP 21945-970, Brazil
IMPA, Instituto de Mathemática Pura e Aplicada, Estrada Dona Castorina, 110, Rio de Janeiro, RJ, CEP 22460-320, Brazil
regi{at}cos.ufrj.br
benar{at}impa.br

We propose a new kind of inexact scheme for a family of generalized proximal point methods for the monotone complementarity problem. These methods, studied by Auslender, Teboulle, and Ben-Tiba, converge under the sole assumption of existence of solutions. We prove convergence of our new scheme and discuss its implementability.

Key Words: Maximal monotone operator; nonlinear complementarity problem; interior proximal point algorithm; extragradient method; enlargement of a maximal monotone operator
History: Received: November 13, 1999; revision received: October 15, 2000;