适用于局部和全局非凸变分优化的对偶原理及相关凸对偶公式

IF 2.4 Q2 ENGINEERING, MECHANICAL
Fabio Silva Botelho
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引用次数: 0

摘要

摘要本文针对物理和工程中的一大类模型,给出了对偶原理、相应的凸对偶公式和适合于非凸原始公式的局部和全局优化的原始对偶公式。结果是基于泛函分析,变分演算和对偶理论的标准工具。特别地,我们开发了对金兹堡-朗道型方程的应用。其他应用包括Burger型方程和Navier-Stokes系统的原始对偶变分公式。我们强调这里的新颖性是,第一个对偶变分公式的发展是凸的原始公式,原来是非凸的。最后,我们还强调了所提出的原始对偶变分公式在其任何临界点周围都有一个大的凸区域。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On duality principles and related convex dual formulations suitable for local and global non-convex variational optimization
Abstract This article develops duality principles, a related convex dual formulation and primal dual formulations suitable for the local and global optimization of non convex primal formulations for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a Ginzburg–Landau type equation. Other applications include primal dual variational formulations for a Burger’s type equation and a Navier–Stokes system. We emphasize the novelty here is that the first dual variational formulation developed is convex for a primal formulation which is originally non-convex. Finally, we also highlight the primal dual variational formulations presented have a large region of convexity around any of their critical points.
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来源期刊
CiteScore
6.20
自引率
3.60%
发文量
49
审稿时长
44 weeks
期刊介绍: The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.
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