The optimization of a multiplier algorithm with NCP function

This paper introduces a new multiplier algorithm that can be used to solve the problems of nonlinear programming with inequality constraints. It first transforms the original problem of an inequality constraint into an equivalent problem of an equality constraint with the Fischer-Burmeister nonlinear complementarity (NCP) function. Subsequently, by using the modified DI PILLO method, the equality constraint problem is transformed into the problem of unconstrained minimization. The solution of the original constraint problem can be obtained by solving a minimum of an unconstrained continuously differentiable function on the basis of an appropriate assumption. The modified inaccurate generalized Newton method is adopted in this paper to solve the problem of the transformed unconstrained minimization.