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

• Published in: Mathematical programming Vol. 194; no. 1-2; pp. 341 - 370
• Main Authors: Dahl, Joachim, Andersen, Erling D.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022; Springer; Springer Nature B.V
• Subjects: Algorithms; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Cones; Full Length Paper; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Mathematics of Computing; Numerical Analysis; Optimization; Theoretical; Exponential-cone optimization; Interior-point methods; Nonsymmetric cone optimization; 90C99
• ISSN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-021-01631-4

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 Tunçel. We specialize Tunçel’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.