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arXiv · 2409.17450

On Strong Quasiconvexity of Functions in Infinite Dimensions

Nguyen Mau Nam·Jacob Sharkansky
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Abstract

In this paper, we explore the concept of $\sigma$-quasiconvexity for functions defined on normed vector spaces. This notion encompasses two important and well-established concepts: quasiconvexity and strong quasiconvexity. We start by analyzing certain operations on functions that preserve $\sigma$-quasiconvexity. Next, we present new results concerning the strong quasiconvexity of norm and Minkowski functions in infinite dimensions. 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.

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Nguyen Mau Nam, Jacob Sharkansky. 2024-09-26. On Strong Quasiconvexity of Functions in Infinite Dimensions. https://arxiv.org/abs/2409.17450

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