A conditional gradient homotopy method with applications to semidefinite programming

IF 2.4 2区 数学 Q1 MATHEMATICS, APPLIED
Pavel Dvurechensky, Gabriele Iommazzo, Shimrit Shtern, Mathias Staudigl
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引用次数: 0

Abstract

We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising as convex relaxations of combinatorial optimization problems. Our method is a double-loop algorithm in which the conic constraint is treated via a self-concordant barrier, and the inner loop employs a conditional gradient algorithm to approximate the analytic central path, while the outer loop updates the accuracy imposed on the temporal solution and the homotopy parameter. Our theoretical iteration complexity is competitive when confronted to state-of-the-art semidefinite programming solvers, with the decisive advantage of cheap projection-free subroutines. Preliminary numerical experiments are provided for illustrating the practical performance of the method.
一个条件梯度同伦方法在半定规划中的应用
提出了一种新的基于同伦的条件梯度方法,用于求解具有大量简单二次约束的凸优化问题。这种模板的实例自然地出现在半定规划问题中,作为组合优化问题的凸松弛。我们的方法是一种双环算法,其中通过自调和屏障处理二次约束,内环采用条件梯度算法近似解析中心路径,而外环更新施加在时间解和同伦参数上的精度。当面对最先进的半确定规划求解器时,我们的理论迭代复杂性具有竞争力,具有廉价的无投影子程序的决定性优势。初步的数值实验说明了该方法的实际性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
IMA Journal of Numerical Analysis
IMA Journal of Numerical Analysis 数学-应用数学
CiteScore
5.30
自引率
4.80%
发文量
79
审稿时长
6-12 weeks
期刊介绍: The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.
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