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A primal-dual interior-point algorithm for nonsymmetric exponential-cone optimization
Mathematical Programming ( IF 2.7 ) Pub Date : 2021-03-09 , DOI: 10.1007/s10107-021-01631-4
Joachim Dahl , Erling D. Andersen

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.



中文翻译:

非对称指数锥优化的原对偶内点算法

提出了一种适用于非对称圆锥优化的新对偶内点算法。它是Nesterov和Todd建议的对称圆锥形情况的著名算法的推广,对Tunçel提出的非对称圆锥使用原始对偶缩放。我们将Tunçel的原始对偶缩放比例专门用于3维指数圆锥的重要情况,从而在标准对称圆锥(例如二次圆锥)算法的水平上得出了一种具有良好数值性能的实用算法。本文的一个重要贡献是新颖的高阶搜索方向,其本质上与用于对称锥算法的Mehrotra校正器相似。在很大程度上,我们提出的算法的效率可以归因于这种新的校正器。

更新日期:2021-03-09
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