On the Interplay among Entropy, Variable Metrics andPotential Functions in Interior-Point Algorithms

Authors:
Levent Tuncel;Michael J. Todd
Affiliations:
Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada;School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853-3801, U.S.A.
Venue:
Computational Optimization and Applications
Year:
1997

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Abstract

We are motivated by the problem of constructing aprimal-dual barrier function whose Hessian induces the (theoreticallyand practically) popular symmetric primal and dual scalings forlinear programming problems. Although this goal is impossible toattain, we show that the primal-dual entropy function may provide asatisfactory alternative. We study primal-dual interior-pointalgorithms whose search directions are obtained from a potentialfunction based on this primal-dual entropy barrier. We providepolynomial iteration bounds for these interior-point algorithms. Thenwe illustrate the connections between the barrier function and areparametrization of the central path equations. Finally, we considerthe possible effects of more general reparametrizations oninfeasible-interior-point algorithms.