An optimization problem
type: Item
instance of: scholarly article
title: An optimization problem
zbMATH Open document ID: 0682.49006
DOI: 10.1007/BF01062900
author: Yanyan Li
published in: Ukrainian Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: Consider the optimization problem: min \(\phi\) (x) for \(x\in S\), where S is the set of solutions to the Hammerstein equation (*) \(x+F_ 1F_ 2(x)=f_ 0\). Under some assumptions on the functional \(\phi\) (properly convex, lower semicontinuous, Gateaux differentiable) and on the operators \(F_ 1\), \(F_ 2\), the author proves that (*) can be regularized in such a way that the regularized problem has a unique solution tending to the solution of the optimization problem as the regularization parameters tend to zero.
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 49J50
zbMATH DE Number: 4117298
zbMATH Keywords: Hammerstein equation
zbMATH Keywords: regularization
MaRDI profile type: Publication
cites work: Sur l'approximation d'équtions et inéquations aux dérivées partielles non linéaires de type monotone
cites work: Q3921739
cites work: Q3907986
cites work: Q4777920
cites work: Nonlinear maximal monotone operators in Banach space
cites work: On the Maximality of Sums of Nonlinear Monotone Operators
description: scientific article; zbMATH DE number 4117298