A nonlinear Lagrangian based on Fischer-Burmeister NCP function

摘要

This paper proposes a nonlinear Lagrangian Based on Fischer-Burmeister NCP function for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. Moreover, the paper develops the dual approach associated with the proposed nonlinear Lagrangian, in which the related duality theorem is demonstrated. Furthermore, it is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Numerical results for solving several nonlinear programming problems are reported, showing that the new nonlinear Lagrangian is superior over other known nonlinear Lagrangians for solving some nonlinear programming problems.