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