Methods of Feasible Directions: A Review

Abstract

Since the theoretical basis for the method of feasible directions (MFD) was originally developed by Zoutendijk in 1960’s, several basic variations and modifications of MFD were proposed and investigated. Even though faster algorithms for solving nonlinear programming problems exist, MFD has never been abandoned because of several important advantages such as the descent property, feasibility of all iterates, conceptual simplicity and overall computational efficiency. In fact, MFD is especially popular in the engineering community where it is heavily used in structural optimization and other engineering design optimization. In engineering design, it is extremely important to end up with a design which satisfies the hard specifications expressed by a set of inequalities. This paper reviews several typical methods of feasible directions and their variants: Zoutendijk’s MFD, Topkis — Veinott’s MFD, Pironneau — Polak’s MFD, Wiest — Polak’s MFD, Cawood — Kostreva’s MFD, Panier — Tits’ FSQP and a modified MFD. Then, the performances of three MFD: Pironneau — Polak’s MFD, Cawood — Kostreva’s MFD and the modified MFD are compared numerically and graphically. The results suggest that the modified MFD is more efficient than the other two MFD.Key wordsnonlinear programmingmethod of feasible directions (MFD)sequential quadratic programming (SQP)direction finding subproblem (DFS)engineering design optimizationstructural optimization