Second-order necessary conditions for differential inclusion problems
type: Item
instance of: scholarly article
title: Second-order necessary conditions for differential inclusion problems
zbMATH Open document ID: 0806.49017
DOI: 10.1007/BF01261988
author: V. Pereyra
published in: Applied Mathematics and Optimization
publication date: 1994-08-10T00:00:00Z
review text: The author considers the following optimal control problem \[ \text{minimize}\quad g(x(T)) \quad\text{subject to } x'(t)\in F(t,x(t)),\;x(0)\in C_ 0,\;x(T)\in C_ 1, \] where \(g\) is Lipschitz continuous, \(C_ 0\) and \(C_ 1\) are closed and convex sets in \(\mathbb{R}^ n\), \(F\) is compact- and convex-valued, integrably Lipschitz in \(x\) and measurable in \(t\) in a tube around a local optimal solution. Second-order necessary conditions are obtained by a suitable approximation of the Clarke normal cone to the reachable set. The approach is based on a paper by \textit{R. T. Rockafellar} [Math. Oper. Res. 14, No. 3, 462-484 (1989; Zbl 0698.90070)].
Mathematics Subject Classification ID: 49K24
zbMATH DE Number: 617357
zbMATH Keywords: differential inclusion
zbMATH Keywords: second-order necessary conditions
zbMATH Keywords: local optimal solution
zbMATH Keywords: Clarke normal cone
reviewed by: A. L. Dontchev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01261988
OpenAlex ID: W2081654798
description: scientific article; zbMATH DE number 617357