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A generalized solution of a nonconvex minimization problem and its stability. (English) Zbl 0626.49013
Author’s abstract: “It is well known that the set of the solutions of a minimization problem on an infinite-dimensional space X is not stable with respect to a perturbation of the minimized function. Here a generalized solution is defined as an element of a suitable completion of X. A necessary and sufficient condition for the completion of X to guarantee the stability of the set of the generalized solutions is given. It is shown that the generalized solution can be considered as a certain minimizing filter on X, which generalizes the notion of the minimizing sequence.”
Reviewer: J.F.Bonnans

49K40 Sensitivity, stability, well-posedness
49J27 Existence theories for problems in abstract spaces
90C48 Programming in abstract spaces
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