Miscellaneous incidences of convergence theories in optimization and nonlinear analysis. I: Behavior of solutions
The author investigates the dependence of the solution set for the inclusion \(y \in F(x)\) in a normed space \(X\) on perturbations of \(y\) and \(F\). For a functional \(f : X \to \overline R\), the behavior of the correspondence \(f \mapsto m_f : = \inf \{f(x) : x \in X\}\) and the multimaps \(f \mapsto S_f : = \{x \in X : f(x) = m_f\}\), \(f \mapsto S_f (\varepsilon) : = \{x \in X : f(x) \leq m_f + \varepsilon\}\) is studied.
scientific article; zbMATH DE number 627475
scientific article