Abstract

The paper examines two methods for the solution of linear programming problems, the simplex method and interior point methods derived from logarithmic barrier methods. Recent improvements to the simplex algorithm, including primal and dual steepest edge algorithms, better degeneracy resolution, better initial bases and improved linear algebra are documented. Logarithmic barrier methods are used to develop primal, dual, and primal-dual interior point methods for linear programming. The primal-dual predictor-corrector algorithm is fully developed. Basis recovery from an optimal interior point is discussed, and computational results are given to document both vast recent improvement in the simplex method and the necessity for both interior point and simplex methods to solve a significant spectrum of large problems

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