On a Dual Direct Cosine Simplex Type Algorithm and Its Computational Behavior

Abstract

The goal of this paper is to propose a dual version of the direct cosine simplex algorithm (DDCA) for general linear problems. The proposed method has not artificial variables, so it is different from both the two-phase method and big-M method. Our technique solves the dual Klee–Minty problem via two iterations and solves the dual Clausen problem via four iterations. The power of the proposed algorithm is evident from the extensive experimental results on benchmark problems adapted from NETLIB. Preliminary results indicate that this dual direct cosine simplex algorithm (DDCA) reduces the number of iterations of the two-phase method.