Existence Results for Generalized Nash Equilibrium Problems under Continuity-Like Properties of Sublevel Sets

Aussel, Didier; Van, Kien Cao; Salas, David

doi:10.1137/20m1353629

Cited by 11 publications

(6 citation statements)

References 20 publications

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“…Let us now give the definition of a "regularity-type" property, inspired from [25] and [20], on the couple of maps (T, K) defining the perturbed variational inequalities considered in this section. Definition 5.1 The couple (T, K) of set-valued maps, with T : X × Λ ⇒ X * and K : U → X will be said to be int-dually lower semicontinuous on X 2 ×Λ× U if for all sequence (y n , z n , λ n , µ n ) n converging to (y, z, λ, µ) ∈ X 2 × Λ × U with y ∈ int K(µ), z ∈ K(µ) and, for any n, y…”

Section: Stability Of Local Solutionsmentioning

confidence: 99%

See 1 more Smart Citation

Existence Results for Quasi-variational Inequalities with Applications to Radner Equilibrium Problems

Aussel

Donato

Milasi

et al. 2021

Set-Valued Var. Anal

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Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for global solutions. Nevertheless, the analysis of such problems found in the literature seems to be very restricted to the global treatment. Motivated by this fact, in this work, we propose local solution concepts, study their interrelations and relations with global concepts and prove existence results as well as stability of local solution map of parametric variational inequalities.The key ingredient of our results is the new concept of local reproducibility of a set-valued map, which we introduce to explore such local solutions to quasivariational inequality problems. As a by-product, we obtain local solutions to quasi-optimization problems, bilevel quasi-optimization problems and Single-Leader-Multi-Follower games.

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Section: Stability Of Local Solutionsmentioning

confidence: 99%

“…As observed in [20], considering regularity conditions on the couple (T, K) instead of on each map T and K separately, as classically done, allows to weaken the hypotheses used to prove some stability results for the solution maps.…”

Section: Stability Of Local Solutionsmentioning

confidence: 99%

Existence Results for Quasi-variational Inequalities with Applications to Radner Equilibrium Problems

Aussel

Donato

Milasi

et al. 2021

Set-Valued Var. Anal

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“…It is important to quote that the existence of such equilibria cannot be guarantee here neither by classical Arrow-Debreu existence result for generalized Nash equilibrium problem (see [1]) nor by the more recent one (see [2]). Indeed, given a vector F −i , the function…”

Section: Defining the Setsmentioning

confidence: 99%

Optimal design of exchange water networks with control inputs in Eco-Industrial Parks

Aussel¹,

Van²,

Salas³

2022

Preprint

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Industrial water conservation is an important adaptation to preserve the environment. Eco-Industrial Parks (EIPs) have been designed to encourage the establishment of water exchange networks between enterprises in order to minimize freshwater consumption and wastewater discharge by maximizing wastewater reuse. This control-input model presents a mathematical programming formulation for designing and optimizing industrial water networks in EIPs, formulating and solving it as a Single-Leader Multi-Follower (SLMF) game problem. Enterprises (followers) aim to minimize their operating costs by reusing wastewater from other enterprises, while the designer (leader) aims to minimize the consumption of natural resources within the ecopark. Moreover, when participating in the ecopark, enterprises can control all their input fluxes and the designer guarantees a minimal relative improvement in comparison with the stand-alone operation of each enterprise. The SLMF game is transformed into a single mixed-integer optimization problem. The obtained results are compared with the results of the blind-input model [21].

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Section: Introductionmentioning

confidence: 99%

“…It is known that when the preference relation is represented by a concave utility function the generalized Nash game can be reformulated as a quasivariational inequality problem, see [3][4][5][6][7]. This reformulation was extended to the quasiconcave case, due to the concept of the normal cone in [6,8,9]. On the other hand, recently, Milasi et al [10], used the variational approach to guarantee the existence of solutions for a competitive economic equilibrium problem, where the consumer preferences are given through a binary relation.…”

Section: Introductionmentioning

confidence: 99%

Generalized Ordinal Nash Games: Variational Approach

Bueno¹,

Cotrina²,

García³

2023

Preprint

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Existence Results for Generalized Nash Equilibrium Problems under Continuity-Like Properties of Sublevel Sets

Cited by 11 publications

References 20 publications

Existence Results for Quasi-variational Inequalities with Applications to Radner Equilibrium Problems

Existence Results for Quasi-variational Inequalities with Applications to Radner Equilibrium Problems

Optimal design of exchange water networks with control inputs in Eco-Industrial Parks

Generalized Ordinal Nash Games: Variational Approach

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