Interior-point methods for reduced Hessian successive quadratic programming

Typical chemical process optimization problems have a large number of equations, but relatively few degrees of freedom. A reduced Hessian successive quadratic programming (rSQP) algorithm has been shown to be successful in solving these types of models efficiently. While the rSQP algorithm reduces the dimension of the QP subproblem solved at each iteration, the number of inequality constraints could still become quite large. As a result, there is still a potentially large combinatorial expense to solving large NLPs with rSQP, as the solution of the QP subproblem is the bottle-neck of the SQP algorithm. To overcome this combinatorial expense, interior-point (IP) methods have been shown to solve large linear programs much faster than the standard simplex method. These interior-point techniques have also been extended to solve quadratic programming problems. For these reasons, we describe an IP method to solve the QP subproblem for rSQP at each iteration. The primal-dual interior-point method is described as well as some higher-order strategies designed to improve convergence. These higher order strategies are evaluated, and also a comparison of several linear equation solvers is made, since the solution of a linear system is required for each interior-point iteration. Finally, we evaluate and compare the new interior-point QP formulation with two standard active-set solvers, QPKWIK and QPOPT, on some industrial-strength NLP problems. (C) 1999 Elsevier Science Ltd. All rights reserved.