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An L1 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,QL1(X,Σ,μ) and q(x)>0 a. e. in X for all qQ. Define R={p/q:pP,qQ}. In this paper we discuss an L1 minimization problem of a nonnegative function E(z,x), i.e. we wish to find a minimum of the functional ϕ(r)=XqE(r,x)dμ form r=p/qR. 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: