Projected dynamical systems in a complementarity formalism
type: Item
instance of: scholarly article
title: Projected dynamical systems in a complementarity formalism
zbMATH Open document ID: 0980.93031
DOI: 10.1016/S0167-6377(00)00042-0
author: W. P. Maurice H. Heemels
author: Johannes M. Schumacher
author: Siep Weiland
published in: Operations Research Letters
publication date: 2002-03-04T00:00:00Z
review text: The authors consider the so-called gradient complementarity systems of differential equations \[ \dot x(t)=- F(x(t))+ [H(x(t))]^T u(t), \] where \(H\) is the Jacobian of \(h\), \(h(x,t): \mathbb{R}^n\to \mathbb{R}^p\), \(0\leq y(t)\perp u(t)\geq 0\). The authors state that such equations belong to the class of projected dynamical equations of the form \[ \dot x(t)= \Pi_K(x(t)- F(x(t))), \] where \(F\) is a vector field, \(K\) is a closed convex set, and \(\Pi_K\) is a projection operator, that prevents the solution from moving outside the constrained set \(K\). The establishment of a connection between the areas of projected dynamical systems and complementarity systems facilitates the transfer of techniques from one domain to the other.
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 1547199
zbMATH Keywords: gradient complementarity systems
zbMATH Keywords: projected dynamical equations
reviewed by: Yuri N. Sankin
MaRDI profile type: Publication
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Wikidata QID: Q126464275
description: scientific article; zbMATH DE number 1547199