On nonlinear minimization problems and Lf-splines. I
type: Item
instance of: scholarly article
title: On nonlinear minimization problems and Lf-splines. I
zbMATH Open document ID: 0541.41038
DOI: 10.1016/0021-9045(83)90094-1
published in: Journal of Approximation Theory
publication date: 1983-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 41A65
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 3859697
zbMATH Keywords: nonlinear minimization problems
zbMATH Keywords: topological spaces
author: D. V. Pai
MaRDI profile type: Publication
full work available at URL: 0021-9045(83)90094-1
OpenAlex ID: W2067667417
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description: scientific article; zbMATH DE number 3859697