黎曼形状芒模中的随机增量拉格朗日法

IF 1.6 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Optimization Theory and Applications Pub Date : 2024-08-21 DOI:10.1007/s10957-024-02488-1

Caroline Geiersbach, Tim Suchan, Kathrin Welker

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引用次数: 0

摘要

在本文中，我们提出了一种（可能是无限维的）黎曼流形上的随机增强拉格朗日方法，用于解决带有有限数量确定性约束的随机优化问题。我们对该方法的收敛性进行了研究，该方法基于随机逼近方法，并将随机停止与更新拉格朗日乘数的迭代程序相结合。我们将该算法应用于具有几何约束的多形状优化问题，并进行了数值演示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds

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Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds

In this paper, we present a stochastic augmented Lagrangian approach on (possibly infinite-dimensional) Riemannian manifolds to solve stochastic optimization problems with a finite number of deterministic constraints. We investigate the convergence of the method, which is based on a stochastic approximation approach with random stopping combined with an iterative procedure for updating Lagrange multipliers. The algorithm is applied to a multi-shape optimization problem with geometric constraints and demonstrated numerically.

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来源期刊

Journal of Optimization Theory and Applications 数学-应用数学

CiteScore

3.30

自引率

5.30%

发文量

149

审稿时长

9.9 months

期刊介绍： The Journal of Optimization Theory and Applications is devoted to the publication of carefully selected regular papers, invited papers, survey papers, technical notes, book notices, and forums that cover mathematical optimization techniques and their applications to science and engineering. Typical theoretical areas include linear, nonlinear, mathematical, and dynamic programming. Among the areas of application covered are mathematical economics, mathematical physics and biology, and aerospace, chemical, civil, electrical, and mechanical engineering.