On nonlinear minimization problems and Lf-splines. I
Let (X,U), (Y,V) be pairs of real linear spaces put in duality by separating bilinear forms \(<\), \(>_{X\times U}\), \(<\), \(>_{Y\times V}\) resp. and equipped with compatible convex topologies, f is a lower semi- continuous proper convex function on Y, T:\(X\to Y\) is a continuous operator and C is a non-empty closed subset of X. Given an element \(y\in Y\), one is concerned here with the minimization problem (Py) \(\alpha =\min_{x\in C}f(Tx-y)\). In this paper there are given some sufficient conditions for problem \((P_ y)\) to have a solution for several kinds of topological spaces.
scientific article; zbMATH DE number 3859697
scientific article