巴拿赫空间中 (D) 型最大单调算子的表示法

IF 1.6 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Optimization Theory and Applications Pub Date : 2024-06-04 DOI:10.1007/s10957-024-02457-8

Bao T. Nguyen, Tran N. Nguyen, Huynh M. Hien

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引用次数: 0

摘要

本文涉及巴拿赫空间中的最大单调算子 A（D），其对偶空间是严格凸的。我们证明了 Ax 的面包含在算子在 x 附近点的有界网的所有弱（^*\）收敛极限的集合中，然后我们利用这个集合得到了 Ax 的表示。此外，我们还给出了基于算子在某些巴拿赫空间中的最小规范选择的 Ax 的支持函数的表示。

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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Representations for Maximal Monotone Operators of Type (D) in Banach Spaces

The present paper deals with a maximal monotone operator A of type (D) in a Banach space whose dual space is strictly convex. We establish some representations for the value Ax at a given point x via its values at nearby points of x. We show that the faces of Ax are contained in the set of all weak\(^*\) convergent limits of bounded nets of the operator at nearby points of x, then we obtain a representation for Ax by use of this set. In addition, representations for the support function of Ax based on the minimal-norm selection of the operator in certain Banach spaces are given.

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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.