An SQP Algorithm with Flexible Penalty Functions

A new penalty function for sequential quadratic programming algorithm is proposed for general nonlinear programming. The quadratic programming sub problem 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. This equality constrained phase uses exact second order information and can be implemented using either a direct solve or an iterative method. The penalty function employs a flexible penalty function 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. This increased flexibility in the step acceptance procedure is designed to promote long productive steps for fast convergence. The paper studies the global convergence properties of the new algorithm and presents a new SQP algorithm with flexible penalty functions by practical performance.