Zur Theorie der Chebyshev-Approximation stetiger Funktionen gibt es eine Reihe ausgezeichneter Lehrb�cher. Behandelt werden dort vor allem Probleme, die in Verallgemeinerung des klassischen Pro� blems der Approximation durch Polynome eine spezielle Vorausset� zung - die sog. Haar-Bedingung - in irgendeiner Form erf�llen, was eine ganze Reihe angenehmer Konsequenzen hat hinsichtlich der Cha� rakterisierung und der Eindeutigkeit der L�sungen. Dies setzt sich fort in den numerischen Verfahren zur Berechnung bester Approxima� tionen, die, wie etwa die bekannten Remes-Verfahren, auf diese speziellen Probleme zugeschnitten sind und bei nicht erf�llter Haar-Bedingung entweder v�llig versagen oder nicht mehr effizient sind. Auf der anderen Seite f�hrt eine ganze Reihe wichtiger An� wendungen auf Probleme, die f�r die Haar-Bedingung nicht erf�llt ist; sei es, da� Funktionen in mehreren Variablen zu approximieren sind, was die Haar-Bedingung grunds�tzlich ausschlie�t, oder da� man wie bei der Behandlung gewisser Randwertprobleme in der Wahl der Ansatzfunktionen nicht frei ist, oder da� die approximierenden Funktionen noch zus�tzliche Nebenbedingungen erf�llen sollen. Das haupts�chliche Anliegen dieses Buches ist es, diese L�cke zu schlie�en und eine Palette derzeit verf�gbarer Methoden darzustel� len, die unter praxisn�heren Voraussetzungen arbeiten. Hierzu bie� tet es sich an, das Approximationsproblem als Optimierungsaufgabe zu formulieren und zu behandeln, da einerseits bei Wegfall der Haar-Bedingung das Chebyshev-Approximationsproblem kaum mehr Struktur als allgemeine Optimierungsprobleme aufweist, und ander� erseits auf diese Art die weit entwickelten, leistungsf�higen Me� thoden der Optimierung f�r die Approximation nutzbar werden.

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