 
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 n1 . So
