ABSTRACT
Chapter 7 addresses the concerns of some peer researchers onthe algorithms reported in Chapters 5 and 6 which have not demonstrated the comparable efficiency to the one enjoyed by Mehrotra'spredictor-corrector algorithm. To show that the arc-search is a better strategy than the line search, an algorithm that mimics Mehrotra'spredictor-corrector algorithm is implemented. The only difference between the two algorithms is that the proposed algorithm uses arc-search and Mehrotra'spredictor-corrector algorithm uses line search. To have a fair comparison, both algorithms are implemented in Matlab, use the same pre-processor and post-processor, start from the same initial point, use the same parameters, and terminate with the same stopping criterion. Since the main cost in computation for both algorithms is to solve linear systems of equations, which is exactly the same for both algorithms, and the arc-search infeasible interior-point algorithm uses less iterations in most tested problems than Mehrotra'spredictor-corrector algorithm, this shows that arc-search infeasible interior-point algorithm is more efficient than Mehrotra'spredictor-corrector algorithm. Beside, the arc-search infeasible interior-point algorithm solves more problems successfully than Mehrotra'spredictor-corrector algorithm, this shows that arc-search infeasible interior-point algorithm is more robust (or stable) than Mehrotra'spredictor-corrector algorithm.
