An Approximately Exact Smooth Penalty Function for Nonlinear Constrained Optimization Problem

Abstract

Penalty functions have important applications in solving constrained optimization problems. In this paper, a new strategy is introduced for smooth approximation of l1 penalty function. We further obtain error estimates between the optimal objective function values of constrained problem and the ones of new smooth penalty problem. As an example, we provide a smooth penalty function for mathematical programming with complementary constraints (MPCC)