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A primal-dual interior-point algorithm for nonsymmetric exponential-cone optimization.

Joachim Dahl(joachim.dahl***at***mosek.com)
Erling Andersen, D.(e.d.andersen***at***mosek.com)

Abstract: A new primal-dual interior-point algorithm applicable to nonsymmetric conic optimization is proposed. It is a generalization of the famous algorithm suggested by Nesterov and Todd for the symmetric conic case, and uses primal-dual scalings for nonsymmetric cones proposed by Tuncel. We specialize Tuncel's primal-dual scalings for the important case of 3 dimensional exponential-cones, resulting in a practical algorithm with good numerical performance, on level with standard symmetric cone (e.g., quadratic cone) algorithms. A significant contribution of the paper is a novel higher-order search direction, similar in spirit to a Mehrotra corrector for symmetric cone algorithms. To a large extent, the efficiency of our proposed algorithm can be attributed to this new corrector.

Keywords: cone programming, exponential cone

Category 1: Linear, Cone and Semidefinite Programming

Citation: Unpublished, Technical Report, May 2019, MOSEK ApS, Fruebjergvej 3, 2100 Copenhagen O, Denmark.

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Entry Submitted: 05/27/2019
Entry Accepted: 05/27/2019
Entry Last Modified: 05/27/2019

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