Necessary optimality conditions for nonconvex differential inclusions with endpoint constraints
type: Item
instance of: scholarly article
title: Necessary optimality conditions for nonconvex differential inclusions with endpoint constraints
zbMATH Open document ID: 0899.49010
author: Yanyan Li
published in: Journal of Differential Equations
publication date: 1996-01-01T00:00:00Z
review text: The problem \(\min g_0(x(1))\) subject to \[ x'(t)\in F(t, x(t)),\quad x(0)= x_0,\quad g_1(x(1))= 0 \] is considered, where \(x\in\mathbb{R}^n\) and values of \(F\) may be nonconvex. A necessary condition (a kind of maximum principle) is derived in terms of Lojasiewicz parametrization of \(\overline{\text{co}} F(t,x)\). When \(F\) admits a \(C^1\) Lojasiewicz representation, this result implies an intrinsic necessary condition (in terms of the Hamiltonian of \(F\) with no explicit use of a parametrization). Comparisons of other known necessary conditions and examples are given. At the end, a theorem is formulated where more general constraints of the form \(g_2(t, x(t))\in A\) are included.
Mathematics Subject Classification ID: 49K24
zbMATH DE Number: 838714
zbMATH Keywords: necessary optimality conditions
zbMATH Keywords: differential inclusions
zbMATH Keywords: maximum principle
zbMATH Keywords: Lojasiewicz parametrization
reviewed by: Tadeusz Rzeżuchowski
MaRDI profile type: Publication
OpenAlex ID: W2052536743
DOI: 10.1006/JDEQ.1996.0006
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description: scientific article; zbMATH DE number 838714