Large-scale decomposition for successive quadratic programming

Abstract

Successive quadratic programming (SQP) has emerged as the algorithm of choice for solving moderately-sized nonlinear process optimization problems. However, as the nonlinear programming problem becomes large (over 100 variables, say) storage requirements for the Hessian matrix and the computational expense of solving large quadratic programs can become prohibitive. To overcome this problem, Westerberg and coworkers proposed two SQP decomposition strategies in 1980 and 1983. The first strategy overcomes this problem but is difficult to implement, while the second has been observed to give inconsistent results. The strategy in this paper uses range and null space projections to develop a decomposition algorithm that is both easy to implement and performs as well as the full SQP algorithm on small problems. This range and null space decomposition (RND) allows for sparse implementations and thus solves large problems easily and reliably. Theoretical development of the RND method is presented as well as a geometric interpretation of this approach compared to others. Finally, a thorough numerical comparison of SQP strategies is presented on a battery of nonlinear programming and process optimization test problems.