Displaying similar documents to “On interior-point methods and simplex method in linear programming.”

A numerical feasible interior point method for linear semidefinite programs

Djamel Benterki, Jean-Pierre Crouzeix, Bachir Merikhi (2007)

RAIRO - Operations Research

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This paper presents a feasible primal algorithm for linear semidefinite programming. The algorithm starts with a strictly feasible solution, but in case where no such a solution is known, an application of the algorithm to an associate problem allows to obtain one. Finally, we present some numerical experiments which show that the algorithm works properly.

A globally convergent non-interior point algorithm with full Newton step for second-order cone programming

Liang Fang, Guoping He, Li Sun (2009)

Applications of Mathematics

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A non-interior point algorithm based on projection for second-order cone programming problems is proposed and analyzed. The main idea of the algorithm is that we cast the complementary equation in the primal-dual optimality conditions as a projection equation. By using this reformulation, we only need to solve a system of linear equations with the same coefficient matrix and compute two simple projections at each iteration, without performing any line search. This algorithm can start...

Rescaled proximal methods for linearly constrained convex problems

Paulo J.S. Silva, Carlos Humes (2007)

RAIRO - Operations Research

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We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner steps even for Linear Programming. This is achieved by using an error criterion that ...

A modified algorithm for the strict feasibility problem

D. Benterki, B. Merikhi (2001)

RAIRO - Operations Research - Recherche Opérationnelle

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In this note, we present a slight modification of an algorithm for the strict feasibility problem. This modification reduces the number of iterations.