Titlebook: Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models; Franco Giannessi,Antonino Maugeri,Panos M. Pardalo Book 20

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Equilibrium Problems and Variational Inequalities,We show that many equilibrium problems fulfill the common laws expressed by a set of conditions and that the equilibrium solution is obtained as a solution to a Variational Inequality. In particular we study the traffic equilibrium problem in the continuum case and we solve the problem to express this problem by means of a Variational Inequality.

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Axiomatization for Approximate Solutions in Optimization,Approximate solutions to optimization problems are characterized by means of properties like consistency, non-emptiness, behaviour w.r.t. inclusion, invariance w.r.t. translation, multiplication.

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Necessary and Sufficient Conditions of Wardrop Type for Vectorial Traffic Equilibria,We consider analogues of Wardrop’s condition for transportation equilibria in the case when the flows and costs are vector-valued. No scalarization is involved.

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Equilibrium in Time Dependent Traffic Networks with Delay,We propose a new model of time dependent traffic networks which include delay effects. Starting from the new definition of “ retarded equilibrium ” we cast the problem in the framework of variational inequalities and give sufficient conditions for the existence of retarded equilibria.

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New Results on Local Minima and Their Applications,In this paper, I give an overview of the rapidly growing research work originated from my recent results on local minima of sequentially weakly lower semicontinuous functionals in reflexive Banach spaces. Particular emphasis is placed on the applications of the basic theory to differential equations.

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https://doi.org/10.1007/978-981-10-6418-0tors in the plane. The operator is assumed to satisfy a suitable ellipticity condition, which allows us to apply nearness theory of mappings. Estimate . having interest in itself, plays a fundamental role.

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