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Volume 1, Issue 3
An $L_1$ Minimization Problem by Generalized Rational Functions

Ying-Guang Shi

J. Comp. Math., 1 (1983), pp. 243-246.

Published online: 1983-01

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  • 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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@Article{JCM-1-243, author = {Ying-Guang Shi}, title = {An $L_1$ Minimization Problem by Generalized Rational Functions}, journal = {Journal of Computational Mathematics}, year = {1983}, volume = {1}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9700.html} }
TY - JOUR T1 - An $L_1$ Minimization Problem by Generalized Rational Functions AU - Ying-Guang Shi JO - Journal of Computational Mathematics VL - 3 SP - 243 EP - 246 PY - 1983 DA - 1983/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9700.html KW - AB -

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.

Ying-Guang Shi. (1983). An $L_1$ Minimization Problem by Generalized Rational Functions. Journal of Computational Mathematics. 1 (3). 243-246. doi:
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