Methods for Nonlinear Constraints in Optimization Calculations

摘要

Ten years ago, the broad consensus among researchers in constrained optimizationwas that sequential quadratic programming (SQP) methods were the methods of choice. While, in the long term, this position may be justified, the past ten years have exposed a number of difficulties with the SQP approach. Moreover, alternative methods have shown themselves capable of solving large-scale problems. In this paper, the authors shall outline the defects with SQP methods, and discuss the alternatives. In particular, the authors shall indicate how their understanding of the subproblems which inevitably arise in constrained optimization calculations has improved. The authors shall also consider the impact of interior-point methods for inequality constrained problems, described elsewhere in this volume, and argue that these methods likely provide a more useful Newton model for such problems than do traditional SQP methods. Finally, the authors shall consider trust-region methods for constrained problems, and the impact of automatic differentiation on algorithm design.