Nonmonotone Line Search Technique for QP-free Infeasible Method

Abstract:

In this paper, a new QP-free infeasible method with nonmonotone line search techniqueis and the Fischer-Burmeister NCP function is proposed for minimizing a smooth function subject to smooth inequality constraints. This iterative method is based on the solution of nonsmooth equations which are obtained by the multiplier function and the Fischer-Burmeister NCP function for the KKT first-order optimality conditions. We use nonmonotone line search techniqueis on line searches. This method is implementable and globally convergent without assuming the strict complementarity condition, isolatedness of the accumulation point and linear independence of the gradients of active constrained functions at the solution. We also prove that the method has superlinear convergence rate under some mild conditions.