Technical Note—Bench Marks Comparing Transportation Codes based on Primal Simplex and Primal-Dual Algorithms

Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems

Primal-Dual Combinatorial Algorithms

Linear program and its duality have long been ubiquitous tools for analyzing NP-hard problems and designing fast approximation algorithms. Plotkin et al proposed a primaldual combinatorial algorithm based on linear duality for fractional packing and covering, which achieves significant speedup on a wide range of problems including multicommodity flow. The key ideas there are: 1) design a primal...

Primal-dual path-following algorithms for circular programming

Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan alg...

Stochastic Inertial primal-dual algorithms

We propose and study a novel stochastic inertial primal-dual approach to solve composite optimization problems. These latter problems arise naturally when learning with penalized regularization schemes. Our analysis provide convergence results in a general setting, that allows to analyze in a unified framework a variety of special cases of interest. Key in our analysis is considering the framew...

A parallel primal-dual simplex algorithm

Recently, the primal–dual simplex method has been used to solve linear programs with a large number of columns. We present a parallel primal–dual simplex algorithm that is capable of solving linear programs with at least an order of magnitude more columns than the previous work. The algorithm repeatedly solves several linear programs in parallel and combines the dual solutions to obtain a new d...