A sufficient condition for the differentiable optimal solution for a problem of Bellman
type: Item
instance of: scholarly article
title: A sufficient condition for the differentiable optimal solution for a problem of Bellman
zbMATH Open document ID: 0773.49011
DOI: 10.1016/0022-247X(92)90296-P
author: Eduardo Camino
author: Oscar Rojo
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: The paper gives a new result concerning the solution of a problem of Bellman: Minimize \(\int_ I(f+g)\) over all pairs \((f,g)\) satisfying \(f(x)+g(y)\geq k(x,y)\), the latter being a continuous kernel. Specifically, it is proved that the problem above has a unique and differentiable solution provided \(k\in C^ 2\) and \(k_{xy}\) does not change its sign on \(I\times I\). The methods used rely on earlier results of the second author.
Mathematics Subject Classification ID: 49K27
zbMATH DE Number: 62884
zbMATH Keywords: integral minimization
zbMATH Keywords: differentiable solution
zbMATH Keywords: Bellman's problem
zbMATH Keywords: continuous kernel
reviewed by: Leszek S. Zaremba
MaRDI profile type: Publication
cites work: An algorithm for approximation of functions
cites work: On an optimization problem of Bellman
description: scientific article; zbMATH DE number 62884