An $L_1$ Minimization Problem by Generalized Rational Functions

An $L_1$ Minimization Problem by Generalized Rational Functions

Year:    1983

Journal of Computational Mathematics, Vol. 1 (1983), Iss. 3 : pp. 243–246

Abstract

Let $P,Q \subset L_1(X,\Sigma,\mu)$ and $q(x)>0$ a. e. in $X$ for all $q\in Q$. Define $R=\{p/q:p\in P,q\in Q\}$. In this paper we discuss an $L_1$ minimization problem of a nonnegative function $E(z,x)$, i.e. we wish to find a minimum of the functional $\phi(r)=\int _X qE(r,x)d\mu$ form $r=p/q\in R$. For such a problem we have established the complete characterizations of its minimum and of uniqueness of its minimum, when both $P,Q$ are arbitrary convex subsets.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1983-JCM-9700

Journal of Computational Mathematics, Vol. 1 (1983), Iss. 3 : pp. 243–246

Published online:    1983-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    4

Keywords: