A maximum theorem for generalized convex functions

Zsolt Páles

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arXiv · 2112.10181

A maximum theorem for generalized convex functions

Zsolt Páles

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Abstract

Motivated by the Maximum Theorem for convex functions (in the setting of linear spaces) and for subadditive functions (in the setting of Abelian semigroups), we establish a Maximum Theorem for the class of generalized convex functions, i.e., for functions $f:X\to \mathbb{R}$ that satisfy the inequality $f(x\circ y)\leq pf(x)+qf(y)$, where $\circ$ is a binary operation on $X$ and $p,q$ are positive constants. As an application, we also obtain an extension of the Karush--Kuhn--Tucker theorem for this class of functions.

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BibTeX RIS

Zsolt Páles. 2021-12-19. A maximum theorem for generalized convex functions. https://arxiv.org/abs/2112.10181

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