Second-order optimality conditions and regularity of Lagrange multipliers for mixed optimal control problems
type: Item
instance of: scholarly article
title: Second-order optimality conditions and regularity of Lagrange multipliers for mixed optimal control problems
zbMATH Open document ID: 1473.49029
author: Yanyan Li
published in: Positivity
publication date: 2021-08-16T00:00:00Z
review text: One considers the following optimal control problem: find a couple of control functions $(u ,v)\in L^{\infty}(\Omega)\times L^{\infty}(\Gamma)$ such that if $y:= y(x;u,v)$ is the solution for the boundary value problem to a semieliptic partial differential equation, \[ Ay=f_1(x,y,u),\text{ in }\Omega,\partial _{\nu _A}y =f_2(x,y,v),\text{ on }\Gamma, \] the following functional gets minimized, \[ F(y;u,v)=\int _{\Omega}L(.,y(.),u(.))dx+\int _ {\Gamma}l(.,y(.),v(.))ds, \] $\min_{\substack {u,v}}F(y;u,v)$. The aim is to look for some second-order optimality conditions. In the second section of the article, there is a review of known results related to second-order necessary optimality conditions and regularity of Lagrange multipliers. One introduces the notion of a strongly optimal solution to the stated problem and under some special assumptions, one proves a result on second-order sufficient optimal conditions for the optimal control problem.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 7382078
zbMATH Keywords: second-order optimality conditions
zbMATH Keywords: Lagrange multiplier
zbMATH Keywords: regularity
zbMATH Keywords: semilinear elliptic equation
zbMATH Keywords: mixed pointwise constant
MaRDI profile type: Publication
full work available at URL: s11117-020-00793-3
OpenAlex ID: W3095001866
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DOI: 10.1007/S11117-020-00793-3
description: scientific article; zbMATH DE number 7382078