Schlesinger M. I.
Minimax theorem for functions on the Carthesian product of branching polylines

The paper proves the minimax theorem for a specific class of functions that are defined on branching polylines in a linear space, not on convex subsets of a linear space. The existence of a saddle point for such functions does not follow directly from the classical minimax theorem and needs individual consideration based both on convex analysis and graph theory. The paper presents a self-sufficient analysis of the problem. It contains everything that enables a plain understanding of the main result and its proof and avoids using concepts outside the scope of obligatory mathematical education of engineers. The paper is addressed to researchers in applied mechanics, engineering, and other applied sciences as well as to mathematicians who lecture convex analysis and optimization methods to non-mathematicians. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: branching polyline, convex analysis, minimax, optimization, saddle point, Graph theory, Branching polyline, Cartesian Products, Convex analysis, Linear spaces, Minimax, Minimax theorem, Optimisations, Polyline, Saddle point, Specific class, Optimization

Cite:
Schlesinger. (2023). Minimax theorem for functions on the Carthesian product of branching polylines. Cybernetics and Systems Analysis, 59 (4), 67–81. doi: https://doi.org/10.1007/s10559-023-00592-0 http://jnas.nbuv.gov.ua/article/UJRN-0001415725