A more complete version of a minimax theorem

2021/03/31 by Biagio Ricceri, Ricceri, Biagio
Computer Science · Decision Sciences · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.2104.00069

openalex publication_date 2021/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we present a more complete version of the minimax theorem established in [7]. As a consequence, we get, for instance, the following result: Let X be a compact, not singleton subset of a normed space (E,‖⋅‖) and let Y be a convex subset of E such that X⊆ Y. Then, for every convex set S⊆ Y dense in Y, for every upper semicontinuous bounded function γ:X→ \bf R and for every λ>4sup_X|γ|\over diam(X), there exists y^*∈ S such that the function x→ γ(x)+λ‖x-y^*‖ has at least two global maxima in X.

Citations

• On a minimax theorem: an improvement, a new proof and an overview of its applications
• Another multiplicity result for the periodic solutions of certain systems

Related

• A non-convex relaxed version of minimax theorems
• On a minimax theorem: an improvement, a new proof and an overview of its applications
• Applying twice a minimax theorem
• A strict minimax inequality criterion and some of its consequences
• Minimax theorems in a fully non-convex setting