梯度微分夹杂的德里赫特问题优化

Elimhan N. Mahmudov, Dilara Mastaliyeva
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引用次数: 0

摘要

本文致力于优化矩形区域上的梯度微分夹杂(DFIs)。离散化方法是求解拟议边界值问题的主要方法。为实现从离散到连续的过渡,提供了一个专门证明的等价定理。为了优化所提出的连续梯度 DFI,离散近似问题中需要通过极限。以欧拉-拉格朗日形式推导出了此类问题最优化的必要条件和充分条件。根据欧拉-拉格朗日邻接包含的发散运算得到的结果被扩展到多维情况。这些结果以局部邻接映射为基础,与莫尔杜霍维奇的 coderivative 概念相关。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Optimization of the Dirichlet problem for gradient differential inclusions

The paper is devoted to optimization of the gradient differential inclusions (DFIs) on a rectangular area. The discretization method is the main method for solving the proposed boundary value problem. For the transition from discrete to continuous, a specially proven equivalence theorem is provided. To optimize the posed continuous gradient DFIs, a passage to the limit is required in the discrete-approximate problem. Necessary and sufficient conditions of optimality for such problems are derived in the Euler–Lagrange form. The results obtained in terms of the divergence operation of the Euler–Lagrange adjoint inclusion are extended to the multidimensional case. Such results are based on locally adjoint mappings, being related coderivative concept of Mordukhovich.

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