Quasi-variational problems with non-self map on Banach spaces: Existence and applications. (October 2022)

• Record Type: Journal Article
• Authors: Allevi, Elisabetta; De Giuli, Maria Elena; Milasi, Monica; Scopelliti, Domenico
• Is Part Of: Nonlinear analysis. Volume 67(2022)
• Publication Date: 2022-10
• Subjects: Generalized quasi-variational inequality -- Projected solution -- Multistage stochastic variational inequality -- Renewable energy market; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103641
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper focuses on the analysis of generalized quasi-variational inequality problems with non-self constraint map. To study such problems, in Aussel et al. (2016) the authors introduced the concept of the projected solution and proved its existence in finite-dimensional spaces. The main contribution of this paper is to prove the existence of a projected solution for generalized quasi-variational inequality problems with non-self constraint map on real Banach spaces. Then, following the multistage stochastic variational approach introduced in Rockafellar and Wets (2017), we introduce the concept of the projected solution in a multistage stochastic setting, and we prove the existence of such a solution. We apply this theoretical result in studying an electricity market with renewable power sources.