PJO: Smoothness of a class of generalized merit functions for the second-order cone complementarity problem

Volume 6
Number 3
pp. 551-571

Smoothness of a class of generalized merit functions for the second-order cone complementarity problem

Sheng-Long Hu, Zheng-Hai Huang and Nan Lu

Abstract

In this paper, we consider the second-order cone complementarity problem (SOCCP). We propose a family of complementarity functions for the second-order cone complementarity problem (SOC C-functions), which contains several popular SOC C-functions as special cases. Based on the new SOC C-functions, a family of merit functions for the SOCCP is proposed. We show that the new merit functions are continuously differentiable and give their derivative formulae. These provide an important theoretical basis for designing some merit function methods to solve the SOCCP. Some preliminary numerical results indicate that the new SOC C-functions and the corresponding merit functions are worth investigating.

Key words	Mathematices Subject Classification
second-order cone, complementarity function, merit function	90C26, 90C30, 90C33

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