Recent improvements to a multiplier-free reduced Hessian successive quadratic programming algorithm

Abstract

Nonlinear programming (NLP) algorithms form the core of many optimization tools in process systems engineering. Over the past 15 years, the successive quadratic programming (SQP) algorithm has been especially useful for a wide variety of processing applications. In particular, the reduced space SQP algorithm has seen many applications to large-scale engineering models. Designed for large NLP problems with few degrees of freedom, this approach has been implemented and applied to engineering problems ranging from flowsheet optimization, on-line process optimization, dynamic systems and even applications with PDE models. This paper describes recent advances in the development of reduced space SQP algorithms. In particular, we investigate several enhancements that improve the efficiency, performance and reliability of these algorithms. Moreover, all of these enhancements preserve the desirable convergence properties shown in our earlier studies. These enhancements are demonstrated on a wide variety of test problems, including scalable mathematical problems, a library of equation-based NLPs and realistic problems in real-time optimization. Results indicate significant performance improvements due to these enhancements.