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A variational approach to the maximization of preferences without numerical representation
No full textOn the study of multistage stochastic vector quasi-variational problems
Full text linkThis paper focuses on the study of multistage stochastic vector generalized quasi-variational inequalities with a variable ordering structure. The proposed multistage stochastic vector quasi-variational problems are defined in a suitable functional setting relative to a finite set of final possible states and certain information fields; these formulations are a multicriteria extension of the multistage stochastic variational inequalities. A relevant aspect of these problems is the presence of the nonanticipativity constraints on the variables of the problem; stage by stage, these constraints impose the measurability with respect to the information field at that stage. Without requiring any assumption of monotonicity, we prove some existence results by using a nonlinear scalarization technique. On this basis, we analyze multistage stochastic vector Nash equilibrium problems: as an example, we focus on a suitable multistage stochastic bicriteria Cournot oligopolistic model
A stochastic variational approach to study economic equilibrium problems under uncertainty
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Solving linear multiplicative programs via branch-and-bound: a computational experience
Full text linkIn this paper, linear multiplicative programs are approached with a branch-and-bound scheme and a detailed computational study is provided. Several underestimation functions are analyzed and various partitioning criteria are presented. A particular class of linear multiplicative programs, useful to solve some applicative bilevel problems, is considered from a theoretical point of view to emphasize an efficient solution method. Detailed results of the computational study are provided to point out the performances provided by using various underestimation functions and partitioning criteria, thus improving some of the results of the current literature
Quasi-variational problems with non-self map on Banach spaces: Existence and applications
No full textThis 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
A VARIATIONAL APPROACH TO WEAKLY CONTINUOUS RELATIONS IN BANACH SPACES
No full textOptimization and equilibrium problems have been extensively studied when the involved preference relations admit a representation by means of real-valued functions. Although these problems have been analyzed under very minimal assumptions on the representation function, this context could appear to be quite restrictive in some practical situations. By using tools of variational analysis and normal operator techniques, very recently some authors have explored the properties of preference relations that do not necessarily admit a numerical representation. However, these contributions are limited to finite-dimensional settings. Our aim in the present work is to develop a new analysis of preference relations in topological spaces and to analyze, in Banach spaces, a suitable concept of a normal operator to the upper contour set. As an application of our theoretical developments, we analyze a particular preference equilibrium problem (of which a preference maximization problem is a particular case) by using a suitable quasi-variational inequality formulation; as an example, a preference allocation problem is also considered
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