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 - <p style="text-align: justify;">Let $P,Q \subset L_1(X,\Sigma,\mu)$ and $q(x)&gt;0$ 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.</p>