A Method for Transforming Non-Convex Optimization Problem to Distributed Form

IF 2.3 3区 数学 Q1 MATHEMATICS
Mathematics Pub Date : 2024-09-09 DOI:10.3390/math12172796
Oleg O. Khamisov, Oleg V. Khamisov, Todor D. Ganchev, Eugene S. Semenkin
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引用次数: 0

Abstract

We propose a novel distributed method for non-convex optimization problems with coupling equality and inequality constraints. This method transforms the optimization problem into a specific form to allow distributed implementation of modified gradient descent and Newton’s methods so that they operate as if they were distributed. We demonstrate that for the proposed distributed method: (i) communications are significantly less time-consuming than oracle calls, (ii) its convergence rate is equivalent to the convergence of Newton’s method concerning oracle calls, and (iii) for the cases when oracle calls are more expensive than communication between agents, the transition from a centralized to a distributed paradigm does not significantly affect computational time. The proposed method is applicable when the objective function is twice differentiable and constraints are differentiable, which holds for a wide range of machine learning methods and optimization setups.
将非凸优化问题转化为分布式形式的方法
我们提出了一种新的分布式方法,用于处理具有耦合相等和不相等约束条件的非凸优化问题。该方法将优化问题转换为特定形式,允许分布式实施修正梯度下降法和牛顿法,使它们像分布式一样运行。我们证明,对于所提出的分布式方法:(i) 通信比调用神谕耗时要少得多;(ii) 它的收敛速度等同于牛顿方法在调用神谕方面的收敛速度;(iii) 对于神谕调用比代理之间的通信更昂贵的情况,从集中式范式过渡到分布式范式不会对计算时间产生显著影响。所提出的方法适用于目标函数两次可微分和约束条件可微分的情况,适用于多种机器学习方法和优化设置。
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
Mathematics
Mathematics Mathematics-General Mathematics
CiteScore
4.00
自引率
16.70%
发文量
4032
审稿时长
21.9 days
期刊介绍: Mathematics (ISSN 2227-7390) is an international, open access journal which provides an advanced forum for studies related to mathematical sciences. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of pure and applied mathematics. Mathematics also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas and new mathematical tools in different branches of mathematics.
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