Smoothing Method for Nonlinear Second-Order Cone Programs with Complementarity Constraints and Its Application to the Smart House Scheduling Problem

Abstract

In this paper, we consider an optimization problem with complementarity constraints and second-order cone constraints. The mathematical program with complementarity constraints (MPCC) has extensively been studied because MPCC has wide application such as engineering design, traffic equilibrium and game theory. Recently, second-order cone programming has also been studied intensively in relation to robust optimization under uncertainty. To the author’s knowledge, however, theoretical and algorithmic results about problems that contain both complementarity and second-order cone constraints have yet to be reported. In this paper, we propose a method for solving nonlinear second-order cone programs with complementarity constraints, which uses a smoothing technique to deal with complementarity constraints, and show its convergence. Moreover, as an application, we formulate a mathematical model of smart house scheduling as a nonlinear second-order cone program with complementarity constraints, and give numerical results with the proposed method.