Nepārtrauktas, gabaliem monotonas funkcijas
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Latvijas Universitāte
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Abstract
Darba mērķis ir izveidot nepārtrauktu, gabaliem monotonu funkciju (NGMF) f:R->R teoriju, un, balstoties uz to, vienkāršot dažu ekstrēmu uzdevumu risināšanu. Īpaša loma tiek atvēlēta monotonitātes signatūrai, ar kuras palīdzību NGMF tiek klasificētas, kā arī teorēmai par NGMF kompozīciju, kurai ir svarīga loma ekstrēmu uzdevumu risināšanā.
In this work author builds a theory of continuous piecewise monotone functions (CPMF)f:R->R with further applications of it in area of mathematical optimization. Concept of monotonicity signature, which allows to classify CPMF, and theorem of CPMF composition – important tool, which allows to simplify solution process of some optimization problems – are the main players here.
In this work author builds a theory of continuous piecewise monotone functions (CPMF)f:R->R with further applications of it in area of mathematical optimization. Concept of monotonicity signature, which allows to classify CPMF, and theorem of CPMF composition – important tool, which allows to simplify solution process of some optimization problems – are the main players here.