Monotonicity Analysis and Recursive Quadratic Programming in Constrained Optimization

Abstract

This paper considers the use of an active set strategy based on monotonicity analysis as an integral part of a recursive quadratic programming (RQP) algorithm for constrained nonlinear optimization. Biggs’ RQP method employing equality constrained subproblems is the basis for the algorithm developed here and requires active set information. The monotonicity analysis strategy is applied to the sequence of search directions selected by the RQP method. As each direction is considered, progress toward optimum occurs and a new constraint is added to the active set. As the active set is finalized the basic RQP method is followed unless a constraint is to be dropped. Testing of the proposed algorithm illustrates its promise as an enhancement to Biggs’ original procedure.