A superlinearly convergent method of feasible directions

Abstract

Method of feasible directions (MFD) is one of the most important methods for solving engineering optimization problems. There exist two types of MFD: one has at most a linear convergence rate and the other has a superlinear convergence rate. The former type includes Zoutendijk's MFD, Topkis–Veinott's MFD, Pironneau–Polak's MFD, Cawood–Kostreva's Norm-Relaxed MFD, and a modified MFD. The latter includes Panier–Tits' FSQP approaches. However, the price of the superlinearly convergent MFD for achieving superlinearity is rather high computational cost per single iteration. This paper presents an algorithm based on the modified MFD. The theoretical analysis shows that this algorithm is locally superlinearly convergent. This algorithm has attained the same convergence rate as FSQP while it only needs to solve two subproblems instead of three subproblems in FSQP. Hence, this algorithm should be computationally more efficient than FSQP.