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Primal-dual potential reduction algorithm for symmetric programming problems with nonlinear objective functions

Leonid Faybusovich(lfaybuso***at***gmail.com)

Abstract: We consider a primal-dual potential reduction algorithm for nonlinear convex optimization problems over symmetric cones. The same complexity estimates as in the case of linear objective function are obtained provided a certain nonlinear system of equations can be solved with a given accuracy. This generalizes the result of K. Kortanek, F. Potra and Y.Ye. We further introduce a generalized Nesterov-Todd direction and show how it can be used to achieve a required accuracy for a class ofnonlinear convex functions satifying scaling Lipschitz condition. This result is a far-reaching generalization of those of F. Potra, Y. Ye and J. Zhu. Finally, we show that a class of functions (which contains quantum entropy function) satisfies scaling Lipschitz condition

Keywords: symmetric cones,convex objective functions, quantum entropy

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Convex and Nonsmooth Optimization

Citation: Preprint, June 2016, Department of Mathematics, University of Notre Dame

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Entry Submitted: 06/24/2016
Entry Accepted: 06/24/2016
Entry Last Modified: 06/24/2016

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