IJPAM: Volume 49, No. 4 (2008)

ON STRONGER FORMS OF FIRST-ORDER NECESSARY
CONDITIONS OF OPTIMALITY FOR
STATE-CONSTRAINED CONTROL PROBLEMS

Sofia O. Lopes$^1$, Fernando A.C.C. Fontes$^2$
$^{1,2}$Department of Mathematics for Science and Technology
University of Minho
Campus de Azurém, Guimarães, 4800-058, PORTUGAL
$^1$e-mail: sofialopes@mct.uminho.pt
$^2$e-mail: ffontes@mct.uminho.pt


Abstract.Recent research in necessary conditions for optimization problems has pursued two main directions. On the one hand, there is a quest to address problems with more and more generality. On the other, there is the investigation of tighter and tighter conditions which are able to identify a reduced set of candidates to minimizers. This work describes a line of research that has been pursued in the latter direction. We discuss the degeneracy phenomenon in optimization problems with inequality constraints. We start by describing this phenomenon in the context of mathematical programming problems. Later, we address the degeneracy phenomenon in the context of optimal control problems. We report some forms of nondegenerate and normal forms of necessary conditions of optimality for optimal control problems with state constraints. A brief overview of some significant literature in this area is made.

Received: August 14, 2008

AMS Subject Classification: 49K15, 49K30

Key Words and Phrases: optimal control, maximum principle, nonlinear systems, constrained systems, constraint qualifications

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 4