Geodesic
On some probabilistic problems of reliability theory with constraint
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 623-638 
G. D. Kartashov. On some probabilistic problems of reliability theory with constraint. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 623-638. http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a2/
@article{TVP_1969_14_4_a2,
     author = {G. D. Kartashov},
     title = {On some probabilistic problems of reliability theory with constraint},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {623--638},
     year = {1969},
     volume = {14},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a2/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $F(x)$ and $G(x)$ be given distribution functions, and $\varphi(y)$ be a known Borel function satisfying (1). The problem under consideration is to minimize the functional $$ \int\,d\pi(x)\int\varphi(y)\,dQ(y\mid x) $$ in $$ Q(y\mid x)\in\mathfrak M(F,G)\cap\mathfrak L(F,G), $$ $\pi(x)$ being a given distribution function with the set of increase points imbedded into that of $F(x)$. Here $\mathfrak M(F,G)$ is the family of conditional distributions $Q(y\mid x)$ satisfying (2) and $\mathfrak L(F,G)$ consists of all $Q(y\mid x)$ with $\int\varphi(y)\,dQ(y\mid x)$ non-decreasing in $x$.