A finite algorithm for globally minimizing a concave function under linear constraints and its applications (Q1090625)

The problem considered is: minimize \(\{\) f(x): \(x\in D\}\) where \(D\subset {\mathbb{R}}^ n\) is a polyhedral convex set not necessarily bounded and \(f: {\mathbb{R}}^ n\to {\mathbb{R}}\) is concave and upper semi-continuous. The solution presented is a development of previous work by \textit{H. Tuy} [Dokl. Akad. Nauk SSSR 159, 32-35 (1964); transl. in Sov. Math. 5, 1437- 1440 (1964)] and by \textit{Nguyen Van Thoai} and \textit{H. Tuy} [Math. Oper. Res 5, 556-566 (1980; Zbl 0472.90054)]. After proving the finiteness of the solution algorithm the author describes applications to the fixed charge problem, bilinear programming and the linear complementarity problem as well as some results of computational experience.