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A nonlinear optimal design problem, with state variable inequality constraints, is solved. The problem is reduced to a Lagrange problem in the Calculus of Variations and necessary conditions are presented. For a certain class of problems, the necessary conditions are reduced to a system of nonlinear algebraic equations which are solved by an iterative procedure. The computational algorithm is efficient and is easily programmed for use on a digital computer.

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No abstract

I n der Arbeit wird das Problem numerisch gelost, diejenige Linearkodination aus einer moglichsf geringen Anzahl gegebener Basisfunkthen zu bestimmen, welche eine vorgegebene Kuwe zwischen einer unteren und einer oberen Grenzkurve i m Sinne des kleinsten Fehlerqwdrats optimal ausgleicht. Es werden Existenz-und Eindeutigkeitssatze und die Anwendung auf eine Vielhml-Aufzeichnung von GammuatraMen angegeben. The problem of finding the linear combination of the fewest possible given basis junctions which simultaneously fits between given continuous upper and lower bounding curves and is the best least spwres fit to a given curve contained between them is solved numerically. Existence and uniqueness theorems are given, and an application to multi-channel recording of gamma radiation datu is mude. B pa6o~e peruaexn npo6ne~a onpegeaemw TaKoro nmeitHoro CoqeTaHm , cocTomuero H a Hamemmero wcna a a~a~~~x ~~~M C H~I X (PYHHUM~~, KoTopoe OnnmanbHo McnpasnHeT a a~a~~y~o KPMBYH) MemAy mmHeii M sepxneit rpaaMsHbIm KPMB~IME~ c TOYKM a p e~n s HaHmemmeit c y m~b~ KsanpaToB O I U M~O K . I I~M B O~H T C X TeopeMbI cywecmosaHm M O~H O~H~~H O C T H a Tamce npmomeme K M H O~O -mHanwoit 3 a n~c~ raMMa-nyseit.