Flexible penalty functions for SQP algorithm with additional equality constrained phase

A flexible penalty function for sequential quadratic programming(SQP) algorithm is proposed for general nonlinear programming. It is based on the quadratic programming subproblem in which each iteration proceeds in two phases. The additional equality constrained phase promotes fast convergence and improves performance in the presence of ill conditioning. The novel feature of the approach is that we employ a flexible penalty function for SQP algorithm with additional equality constrained phase. The flexible penalty function is to promote convergence, where during each iteration the penalty parameter can be chosen as any number within a prescribed interval, rather than a fixed value. The paper studies the global and local convergence properties of the new algorithm and presents a set of numerical experiments to illustrate its practical performance.