Second-order necessary conditions in a domain optimization problem
type: Item
instance of: scholarly article
title: Second-order necessary conditions in a domain optimization problem
zbMATH Open document ID: 0675.49021
DOI: 10.1007/BF01102343
author: S. H. Smith
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: Second-order necessary conditions of the Kuhn-Tucker type for optimality in a domain optimization problem are studied. The second variation, corresponding to a boundary variation, of the solution to a boundary- value problem is shown to exist and is given as the solution of a boundary-value problem of the same type. The boundary data are shown to be given in terms of the solution and the first variation of the solution. From these results, the second variation of the objective function is calculated to derive second-order necessary conditions of the Kuhn-Tucker type.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 4105716
zbMATH Keywords: second-order necessary conditions
zbMATH Keywords: Kuhn-Tucker type
zbMATH Keywords: domain optimization
zbMATH Keywords: second variation
zbMATH Keywords: boundary variation
MaRDI profile type: Publication
cites work: Torsional rigidity, principal frequency, electrostatic capacity and symmetrization
cites work: Optimization of elastic bars in torsion
cites work: Convexity of domain functionals
cites work: Necessary Conditions for a Domain Optimization Problem in Elliptic Boundary Value Problems
cites work: Shape sensitivity analysis of an elastic-plastic torsion problem
cites work: Variational approach by means of adjoint systems to structural optimization and sensitivity analysis. II. Structure shape variation
cites work: Q3317635
cites work: Q5187597
cites work: Q3280274
cites work: On the existence of a solution in a domain identification problem
cites work: Lower-semicontinuity in domain optimization problems
Recommended article: Second Order Necessary Conditions in Optimization
Recommended article: Second-order optimality conditions for constrained domain optimization
Recommended article: Second-order necessary and sufficient conditions in nonsmooth optimization
Recommended article: Q4877761
Recommended article: Second-order necessary conditions in semismooth optimization
Recommended article: Q4250857
Recommended article: Second-Order Necessary Conditions in Constrained Semismooth Optimization
Recommended article: Second-Order Conditions for Optimization Problems with Constraints
Recommended article: Second-order necessary conditions for optimality in nonsmooth nonlinear programming
Recommended article: Q4244568
description: scientific article; zbMATH DE number 4105716