A decomposition method for the min concave cost flow problem with a staircase structure

We consider the min concave cost flow problem with a staircase structure. A method is presented for decomposing this problem into a sequence of much smaller subproblems.

[1]  Leon S. Lasdon,et al.  Optimization Theory of Large Systems , 1970 .

[2]  W. Zangwill.  Minimum Concave Cost Flows in Certain Networks , 1968 .

[3]  G. Gallo,et al.  Adjacent extreme flows and application to min concave cost flow problems , 1979, Networks.

[4]  Hoang Tuy,et al.  Concave minimization under linear constraints with special structure , 1985 .

[5]  H. Tuy.  Global Minimization of a Difference of Two Convex Functions , 1987 .

[6]  T. V. Thieu.  A finite method for globally minimizing a concave function over an unbounded polyhedral convex set and its applications , 1988 .

[7]  Giorgio Gallo,et al.  Lower planes for the network design problem , 1983, Networks.

[8]  R. Horst,et al.  On finding new vertices and redundant constraints in cutting plane algorithms for global optimization , 1988 .

[9]  Norman Zadeh,et al.  On building minimum cost communication networks , 1973, Networks.

[10]  Panos M. Pardalos,et al.  Global minimization of large-scale constrained concave quadratic problems by separable programming , 1986, Math. Program..

[11]  A. Fiacco,et al.  Convexity and concavity properties of the optimal value function in parametric nonlinear programming , 1983 .

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

[13]  Bernard Yaged,et al.  Minimum cost routing for static network models , 1971, Networks.

[14]  A. M. Geoffrion.  Generalized Benders decomposition , 1972 .

[15]  Thomas L. Magnanti,et al.  Tailoring Benders decomposition for uncapacitated network design , 1986 .

[16]  Giorgio Gallo,et al.  An algorithm for the min concave cost flow problem , 1980 .

[17]  Jan Karel Lenstra,et al.  The complexity of the network design problem , 1978, Networks.

[18]  Richard M. Soland,et al.  Optimal Facility Location with Concave Costs , 1974, Oper. Res..