A New Penalty Method for Nonlinear Programming

Penalty function methods, presented many years ago, play exceedingly important roles in the optimization community. According to numerical results, penalty function approaches work very efficiently for equality constrained problems. For inequality constrained problems, sequential quadratic programming (SQP) approaches do better than that of sequential penalty quadratical programming (SlQP) methods. Taking these into account, we propose another optimization approach, in which we aim to combine the advantages of penalty function techniques and SQP approaches. In the new technique, equality constraints are handled by penalty function technique, while inequality constraints are still treated as constraints. The corresponding theories are exploited in this work. The theories of the corresponding augmented Lagrangian function, especially quadratic augmented penalty methods, are also achieved. A new kind of penalty method, combining the advantages of SQP and SlQP, is therefore developed in this work.