A GENERALIZED SOLUTION OF A NONCONVEX MINIMIZATION PROBLEM AND ITS STABILITY
Tomáš Roubı́ček · Czech digital mathematics library · 1986
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\o 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.