Nonlinear Lagrangians for Nonlinear Programming Based on Modified Fischer-Burmeister NCP Functions (Journal of Computational Mathematics, 2018)
This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCPfunctions for solving nonlinear programming problems with inequality constraints. Theconvergence theorem shows that the sequence of points generated by this nonlinear Lagrange algorithm is locally convergent when the penalty parameter is less than a thresholdunder a set of suitable conditions on problem functions, and the error bound of solution,depending on the penalty parameter, is also established. It is shown that the conditionnumber of the nonlinear Lagrangian Hessian at the optimal solution is proportional to thecontrolling penalty parameter. Moreover, the paper develops the dual algorithm associated with the proposed nonlinear Lagrangians. Numerical results reported suggest thatthe dual algorithm based on proposed nonlinear Lagrangians is effective for solving somenonlinear optimization problems.