Two Classes of Merit Functions for Infinite-Dimensional Second Order Complimentary Problems

Abstract

In this article, we extend two classes of merit functions for the second-order complementarity problem (SOCP) to infinite-dimensional SOCP. These two classes of merit functions include several popular merit functions, which are used in nonlinear complementarity problem, (NCP)/(SDCP) semidefinite complementarity problem, and SOCP, as special cases. We give conditions under which the infinite-dimensional SOCP has a unique solution and show that all these merit functions provide an error bound for infinite-dimensional SOCP and have bounded level sets. These results are very useful for designing solution methods for infinite-dimensional SOCP.