Titlebook: Recent Developments in Well-Posed Variational Problems; Roberto Lucchetti,Julian Revalski Book 1995 Springer Science+Business Media Dordre

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Well-Posedness for Nash Equilibria and Related Topics,Most of this survey is in the context of non-cooperative games in strategic form, and is essentially devoted to concepts which gravitate around the idea of Nash equilibrium (briefly: NE): for standard terminology in game theory and for general reference, see [36] or [13].

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Well-Posed Problems in the Calculus of Variations,A scalar minimization problem is called . if there exists a unique solution which either attracts every minimizing sequence (according to a definition firstly isolated by Tikhonov), or depends continuously upon problem’s data (according to the classical notion which goes back to Hadamard), or both.

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Generic Well-Posedness of Optimization Problems and the Banach-Mazur Game, equipped with the sup-norm ||f||. = sup{| .)|: .}, .), becomes a Banach space. Each .) determines a minimization problem: find x. ∈ . with ..) = inf {.} =: inf (.). We designate this problem by (.). Among the different properties of the minimization problem (.) the following ones are of special interest in the theory of optimization:

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Set-Valued Interpolation, Differential Inclusions, and Sensitivity in Optimization,sdorff distance. The connection between order of convergence results and sensitivity properties of finite-dimensional convex optimization problems is discussed. The results are applied to the numerical approximation of reachable sets of linear control problems by quadrature formulae and interpolation techniques for set-valued mappings.