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Doubles limites ordonnées et théorèmes de minimax

Marc De Wilde (1974)

Annales de l'institut Fourier

On introduit une variante des “doubles limites interchangeables” de Grothendieck, les “doubles limites ordonnées” et on en déduit un théorème de maximinimax. En introduisant des conditions de convexité convenables, on transforme celui-ci en un théorème de minimax. Ces résultats permettant de retrouver de façon simple un théorème de maximinimax de Simons.

Event-triggered design for multi-agent optimal consensus of Euler-Lagrangian systems

Xue-Fang Wang, Zhenhua Deng, Song Ma, Xian Du (2017)


In this paper, a distributed optimal consensus problem is investigated to achieve the optimization of the sum of local cost function for a group of agents in the Euler-Lagrangian (EL) system form. We consider that the local cost function of each agent is only known by itself and cannot be shared with others, which brings challenges in this distributed optimization problem. A novel gradient-based distributed continuous-time algorithm with the parameters of EL system is proposed, which takes the distributed...

Existence of solutions to weak nonlinear bilevel problems via MinSup and d.c. problems

Abdelmalek Aboussoror, Abdelatif Mansouri (2008)

RAIRO - Operations Research

In this paper, which is an extension of [4], we first show the existence of solutions to a class of Min Sup problems with linked constraints, which satisfy a certain property. Then, we apply our result to a class of weak nonlinear bilevel problems. Furthermore, for such a class of bilevel problems, we give a relationship with appropriate d.c. problems concerning the existence of solutions.

Minimax control of nonlinear evolution equations

Nikolaos S. Papageorgiou (1995)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study the minimax control of systems governed by a nonlinear evolution inclusion of the subdifferential type. Using some continuity and lower semicontinuity results for the solution map and the cost functional respectively, we are able to establish the existence of an optimal control. The abstract results are then applied to obstacle problems, semilinear systems with weakly varying coefficients (e.gȯscillating coefficients) and differential variational inequalities.

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