PIECEWISE LINEAR NCP FUNCTION FOR QP FREE FEASIBLE METHOD

Abstract. In this paper, a QP-free feasible method with piecewise NCP functions is proposed for nonlinear inequality constrained optimization problems. The new NCP functions are piece-wise linear-rational, regular pseudo-smooth and have nice properties. This method is based on the solutions of linear systems of equation reformulation of KKT optimality conditions, by using the piecewise NCP functions. This method is implementable and globally convergent without assuming the strict complementarity condition, the isolatedness of accumulation points. Fur-thermore, the gradients of active constraints are not requested to be linearly independent. The submatrix which may be obtained by quasi-Newton methods, is not requested to be uniformly positive definite. Preliminary numerical results indicate that this new QP-free method is quite promising. Consider the constrained nonlinear optimization problem (NLP) min f(x), x ∈ Rn, s.t. G(x) ≤ 0, (1) where f: Rn → R andG(x) = (g1(x), g2(x),..., gm(x))T: Rn → Rm are Lipchitz continuously differentiable functions