A relaxed reduced space SQP strategy for dynamic optimization problems

Abstract: "Recently, strategies have been developed to solve dynamic simulation and optimization problems in a simultaneous manner by applying orthogonal collocation on finite elements and solving the nonlinear program (NLP) with a reduced space Successive Quadratic Programming (SQP) approach. In this paper we develop a relaxed simultaneous approach that leads to faster performance. The method operates in the reduced space of the control variables and solves the collocation equations inexactly at each SQP iteration. Unlike previous simultaneous formulations, it is able to consider the state variables one element at a time. Also, this approach is compared on two process examples to the reduced gradient, feasible path approach outlined in Logsdon and Biegler (1992). Here nonlinear programs with up to 5500 variables are solved with only 40% of the effort. Finally, a theoretical analysis of this approach is provided."