Optimal control and invexity
type: Item
instance of: scholarly article
title: Optimal control and invexity
zbMATH Open document ID: 0911.49021
DOI: 10.1016/S0898-1221(98)00002-9
publication date: 1998-08-20T00:00:00Z
review text: The following fixed-time optimal control problem is considered: \[ \text{minimize}\quad F(x,y):= \int^T_0 f(x(t), u(t),t)dt \] \[ \text{subject to}\quad x(0)= x_0,\;x(t)= m(x(t), u(t), t),\;u(t)\in \Gamma(t),\quad 0\leq t\leq T, \] where \(f\), \(m\) are functions from \(C^1\), \(\Gamma(t)\) is a given set, \(x(.)\) is piecewise smooth, \(u(.)\) is piecewise continuous. Under a suitable invexity hypothesis, the sufficiency of Karush-Kuhn-Tucker conditions for a local and under certain additional conditions even for a global minimum is proved. Some duality results are obtained.
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 90C99
zbMATH DE Number: 1192722
zbMATH Keywords: constrained minimization
zbMATH Keywords: fixed-time optimal control problem
zbMATH Keywords: invexity
zbMATH Keywords: Karush-Kuhn-Tucker conditions
zbMATH Keywords: duality
author: B. D. Craven
reviewed by: Karel Zimmermann
MaRDI profile type: Publication
cites work: Q3869074
cites work: Q4866631
cites work: On sufficiency of the Kuhn-Tucker conditions
cites work: On generalised convex mathematical programming
full work available at URL: s0898-1221(98)00002-9
OpenAlex ID: W2093815419
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1192722