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<p><?tk 4?>In this paper, we study the concept of strong quasiconvexity for functions defined on normed vector spaces. We begin by examining operations that preserve strong quasiconvexity. We then establish new results on the strong quasiconvexity of norm functions in infinite-dimensional settings. Furthermore, we extend a recent result by Lara (J Optim Theory Appl 192:891–911, 2022) 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.</p>

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On strong quasiconvexity of functions in infinite dimensions

  • 期刊论文

  • 发表日期：

    2025年10月23日

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  • Nguyen Mau Nam,
  • Jacob Sharkansky

摘要

In this paper, we study the concept of strong quasiconvexity for functions defined on normed vector spaces. We begin by examining operations that preserve strong quasiconvexity. We then establish new results on the strong quasiconvexity of norm functions in infinite-dimensional settings. Furthermore, we extend a recent result by Lara (J Optim Theory Appl 192:891–911, 2022) 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.