无限维函数的强准凸性
最优化与控制
2024-11-12 v2
摘要
本文探讨了定义在规范向量空间上的函数的σ-准凸性概念。这种概念涵盖了两种重要且广为人知的概念：准凸性和强准凸性。我们首先分析了保持σ-准凸性的函数的某些操作。接着，我们提出了关于规范函数和Minkowski函数在无限维中强准凸性的新结果。 Furthermore, we extend a recent result by F. Lara [16] on the supercoercive properties of strongly quasiconvex functions, with applications to the existence and uniqueness of minima, from finite dimensions to infinite dimensions. Finally, we address counterexamples related to strong quasiconvexity.
关键词
引用
@article{arxiv.2409.17450,
title = {On Strong Quasiconvexity of Functions in Infinite Dimensions},
author = {Nguyen Mau Nam and Jacob Sharkansky},
journal= {arXiv preprint arXiv:2409.17450},
year = {2024}
}