Interior-point methods for reduced Hessian successive quadratic programming

Typical chemical process optimization problems have a large number of equat ions, but relatively few degrees of freedom. A reduced Hessian successive q uadratic programming (rSQP) algorithm has been shown to be successful in so lving these types of models efficiently. While the rSQP algorithm reduces t he dimension of the QP subproblem solved at each iteration, the number of i nequality 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 a lgorithm. To overcome this combinatorial expense, interior-point (IP) metho ds have been shown to solve large linear programs much faster than the stan dard simplex method. These interior-point techniques have also been extende d to solve quadratic programming problems. For these reasons, we describe a n IP method to solve the QP subproblem for rSQP at each iteration. The prim al-dual interior-point method is described as well as some higher-order str ategies 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 form ulation with two standard active-set solvers, QPKWIK and QPOPT, on some ind ustrial-strength NLP problems. (C) 1999 Elsevier Science Ltd. All rights re served.