The concept of projected solution has been introduced in Aussel et al. (J Optim Theory Appl 170:818-837, 2016) for studying quasivariational problems where the constraint map may not be a self-map. Aim of this paper is to establish a new result on the existence of projected solutions for finite-dimensional quasiequilibrium problems without any monotonicity assumptions and without assuming the compactness of the feasible set. These two facts allow us to improve some recent results. Additionally, we deduce the existence of projected solutions for quasivariational inequalities, quasioptimization problems and generalized Nash equilibrium problems. Also, a comparison with similar results is provided.
Projected solutions for finite-dimensional quasiequilibrium problems
Castellani M.;Giuli M.
;Latini S.
2023-01-01
Abstract
The concept of projected solution has been introduced in Aussel et al. (J Optim Theory Appl 170:818-837, 2016) for studying quasivariational problems where the constraint map may not be a self-map. Aim of this paper is to establish a new result on the existence of projected solutions for finite-dimensional quasiequilibrium problems without any monotonicity assumptions and without assuming the compactness of the feasible set. These two facts allow us to improve some recent results. Additionally, we deduce the existence of projected solutions for quasivariational inequalities, quasioptimization problems and generalized Nash equilibrium problems. Also, a comparison with similar results is provided.Pubblicazioni consigliate
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