When successive quadratic programming methods are used in connection
with the sequential-modular or simultaneous-modular approaches to chemical
process optimization, substantial reductions in calculation time can be
achieved by reducing the number of derivative evaluations. We present here
methods for achieving such a reduction; these include two second-order
correction techniques and a selection strategy. One second-order correction
technique is a variation of the method of Fletcher. The other involves
a correction quadratic program (QP) with a Broyden-updated constraint Jacobian.
This correction step solves a QP subject to the next quasi-Newton approximation
to the solution of the currently active constraints. The selection strategy
forces the methods to work together to provide the most progress in a given
iteration. An iteration could involve only a basic step, a basic step plus
either second-order correction step, or a combination of the basic step
and both correction steps. Backtrack capabilities allow the program to
abandon a nonproductive correction step and recover the base QP step. Tests
on both general problems and flowsheeting problems show these techniques
to provide a reduction in the number of derivative evaluations required
in most cases.
Comput. Chem. Eng., 16, 901-915 (1992)