Summary: Approximation and Optimization:
Classical results and new developments
G. Still, University of Twente
Abstract. It is a common concept to treat Chebyshev approximation as a semi­infinite
problem. We give a concise survey of the classical approach and discuss new develop­
ments. In particular, reverse approximation problems are treated as a special instances of
semi­infinite problems with variable index sets. We consider theoretical and numerical
aspects as well as applications.
Keywords: Chebyshev approximation, Semi­infinite programming
Mathematical Subject Classification 1991: 90C34, 90C31
1. Introduction
It is a common approach to consider Chebyshev approximation in the context of
semi­infinite programming. See e.g. [14] and [5]. This paper intends to give a
summary of this concept. We review earlier results but also discuss new develop­
ments. In particular the class of reverse approximation problems and the related
new topic of semi­infinite programs with variable index sets are presented. We
consider theoretical and numerical aspects as well as applications.
Approximation theory deals with problems of the following form. A function
h : B # R, continuous on the compact subset B # R m , has to be approximated
by a continuous function a : X × B # R where X is an open subset of R n-1 . So

Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente
Still, Georg - Department of Applied Mathematics, Universiteit Twente

Collections: Engineering; Mathematics