A Conical Algorithm for Globally Minimizing a Concave Function Over a Closed Convex Set

In this paper we are concerned with the problem of finding the global minimum of a concave function over a closed, convex, possibly unbounded set in R n . The intrinsic difficulty of this problem is due to the fact that a local minimum of the objective function may fail to be a global one---which makes the conventional methods of local optimization almost useless.

[1]  Karla L. Hoffman,et al.  A method for globally minimizing concave functions over convex sets , 1981, Math. Program..

[2]  Giorgio Gallo,et al.  Bilinear programming: An exact algorithm , 1977, Math. Program..

[3]  S. E. Jacobsen,et al.  Linear programs with an additional reverse convex constraint , 1980 .

[4]  Max Rössler.  Eine Methode zur Berechnung des optimalen Produktionsprogramms bei konkaver Zielfunktion , 1971, Unternehmensforschung.

[5]  Andrew B. Whinston,et al.  Optimization over Leontief substitution systems , 1975 .

[6]  Alan M. Frieze,et al.  A bilinear programming formulation of the 3-dimensional assignment problem , 1974, Math. Program..

[7]  Reiner Horst,et al.  An algorithm for nonconvex programming problems , 1976, Math. Program..

[8]  O. Mangasarian.  Characterization of linear complementarity problems as linear programs , 1978 .

[9]  S. E. Jacobsen,et al.  Reverse convex programming , 1980 .

[10]  Nguyen V. Thoai,et al.  Convergent Algorithms for Minimizing a Concave Function , 1980, Math. Oper. Res..

[11]  Willard I. Zangwill,et al.  A Deterministic Multiproduct, Multi-Facility Production and Inventory Model , 1966, Oper. Res..

[12]  Ferenc Forgó.  Cutting plane methods for solving nonconvex programming problems , 1972, Acta Cybern..

[13]  Arthur F. Veinott,et al.  Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems , 1969, Oper. Res..

[14]  James E. Falk,et al.  A Successive Underestimation Method for Concave Minimization Problems , 1976, Math. Oper. Res..