We analyze the multiple cut generation scheme in the analytic center cutting plane method. We propose an optimal primal and dual updating direction when the cuts are central. The direction is optimal in the sense that it maximizes the product of the new dual slacks and of the new primal variables within the trust regions defined by Dikin’s primal and dual ellipsoids. The new primal and dual dir...

Objective: This study aims to find and compare the effects of primal reflex release technique and stretching exercises on pain intensity, functional performance, and pain-free sitting duration in patients with coccydynia. Methods: This is a randomized clinical trial. A total of 46 individuals were chosen for the sample based on the inclusion criteria, and they were divided into groups A and B....

Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic ...

Last time we discussed how LP-duality can be applied to approximation. We introduced the primaldual method for approximating the optimal solution to an LP in a combinatorial way. We applied this technique to give another 2-approximation for the Vertex Cover problem. In this lecture, we present and analyze a primal-dual algorithm that gives a 2-approximation for the Steiner Forest problem. We al...

In this paper, we present a new primal-dual interior-point algorithm for linear optimization based on a trigonometric kernel function. By simple analysis, we derive the worst case complexity for a large-update primal-dual interior-point method based on this kernel function. This complexity estimate improves a result from [1] and matches the one obtained in [2].

We study monotonicity of primal and dual objective values in the framework of primal-dual interior-point methods. The primal-dual aane-scaling algorithm is monotone in both objectives. We derive a condition under which a primal-dualinterior-point algorithm with a centering component is monotone. Then we propose primal-dual algorithms that are monotone in both primal and dual objective values an...