(untitled) (Journal of Computational Mathematics, 1983)
Let P,Q L_1(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 L_1 minimization problem of a nonnegative function E(z,x), i.e. we wish to find a minimum of the functional φ(r)=_X qE(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.