Mathematics > Optimization and Control
[Submitted on 15 Oct 2023 (v1), last revised 30 Jul 2024 (this version, v2)]
Title:Best-response algorithms for a class of monotone Nash equilibrium problems with mixed-integer variables
View PDF HTML (experimental)Abstract:We characterize the convergence properties of traditional best-response (BR) algorithms in computing solutions to mixed-integer Nash equilibrium problems (MI-NEPs) that turn into a class of monotone Nash equilibrium problems (NEPs) once relaxed the integer restrictions. We show that the sequence produced by a Jacobi/Gauss-Seidel BR method always approaches a bounded region containing the entire solution set of the MI-NEP, whose tightness depends on the problem data, and it is related to the degree of strong monotonicity of the relaxed NEP. When the underlying algorithm is applied to the relaxed NEP, we establish data-dependent complexity results characterizing its convergence to the unique solution of the NEP. In addition, we derive one of the very few sufficient conditions for the existence of solutions to MI-NEPs. The theoretical results developed bring important practical benefits, illustrated on a numerical instance of a smart building control application.
Submission history
From: Filippo Fabiani [view email][v1] Sun, 15 Oct 2023 16:50:52 UTC (1,517 KB)
[v2] Tue, 30 Jul 2024 06:01:43 UTC (1,207 KB)
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