3-1 Piecewise NCP Function for New Nonmonotone QP-Free Infeasible Method

Algorithm flow chart We propose a nonmonotone QP-free infeasible method for inequality-constrained nonlinear optimization problems based on a 3-1 piecewise linear NCP function. This nonmonotone QP-free infeasible method is iterative and is based on nonsmooth reformulation of KKT first-order optimality conditions. It does not use a penalty function or a filter in nonmonotone line searches. This algorithm solves only two systems of linear equations with the same nonsingular coefficient matrix, and is implementable and globally convergent without a linear independence constraint qualification or a strict complementarity condition. Preliminary numerical results are presented.