CONVERGENCE TO A SECOND-ORDER CRITICAL POINT BY A TRUST-REGION SQP METHOD WITH A NONSMOOTH MERIT FUNCTION

Abstract

In this paper, we deal with a trust-region sequential quadratic programming (SQP) method with a nonsmooth merit function for solving nonlinear optimization poblems. Based on the method proposed by Yamashita and Dan (2005), our method calculates search directions by solving the two types of subproblems, which are a convex QP subproblem and a linear system of equations. When possible, we execute a search along the negative-curvature direction. The proposed method generates negative-curvature directions in the existence of the nonsmooth term in the merit function. We show that the generated sequence converges to a point that satisfies the first-order and second-order optimality conditions.