Abstract
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.
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A.V. Fiacco and J. Kyparisis, Convexity and concavity properties of the optimal value function in parametric nonlinear programming. J. Optim. Theory Appl.,48(1986), 95–126.
G. Gallo and C. Sodini, Adjacent extreme flow and application to min concave cost flow problems. Networks9(1979), 95–121.
G. Gallo, C. Sandi and C. Sodini, An algorithm for the min concave cost flow problem. European J. Oper. Res.,4(1980), 248–255.
G. Gallo, Lower planes for the network design problem. Networks13(1983), 411–426.
A.M. Geoffrion, Generalized Benders decomposition. J. Optim. Theory. Appl.,10(1972), 237–260.
K.L. Hoffman, A Method for globally minimizing concave functions over convex sets. Math. Programming,20(1981), 22–32.
R. Horst, J. de Vries and N.V. Thoai, On finding new vertices and redundant constraints in cutting plane algorithms for global optimization. Oper. Res. Lett.,7(1988), 85–90.
D.S. Johnson, J.K. Lenstra and A.H.G. Rinnooy Kan, The complexity of the network design problem. Networks,8(1978), 279–285.
L.S. Lasdon, Optimization Theory for Large Systems. The Macmillan Company, New York, New York, 1970.
T.L. Magnanti, P. Mireault and R.T. Wong, Tailoring Benders decomposition for uncapacitated network design. Math. Programming Stud.,26(1986), 112–154.
P. Rech and L.G. Barton, A nonconvex transportation algorithm. Applications of Mathematical Programming Techniques (ed. EML Beale), 250–260.
J.B. Rosen and P.M. Pardalos, Global minimization of large-scale constrained concave quadratic problems by separable programming. Math. Programming,34(1986), 163–174.
R.M. Soland, Optimal facility location with concave cost. Oper. Res.,22(1974), 373–382.
P.T. Thach, Concave minimization under nonconvex constraints with special structure. Essays on nonlinear Analysis and Optimization Problems, Hanoi Inst. Math. Press, 1987, 121–139.
P.T. Thach, A decomposition method using a pricing, mechanism for min concave cost flow problems with the hierarchical structure. Math. Programming (submitted).
T.V. Thieu, B.T. Tam and V.T. Ban, An outer approximation method for globally minimizing a concave function over a compact convex set. Acta Math. Vietnam.,8(1983), 21–40.
H. Tuy, Concave minimization under linear constraints with special, structure. Optimization,16(1985), 335–352.
H. Tuy, Global minimization of a difference of two convex functions. Math. Programming Stud.,30(1987), 150–182.
H. Tuy, On polyhedral annexation method for concave minimization. Volume Dedicated to the Memory of L.V. Kantorovich, Amer. Math. Soc. (to appear).
D.A. Wismer, Optimization Methods for Largescale Systems with Applications. McGraw-Hill Book Company, New York, New York, 1971.
B.J. Yaged, Minimum cost routing for network models. Networks,1(1971), 139–172.
N. Zadel, On building minimum cost communication networks. Networks,3(1973), 315–331.
W.I. Zangwill, Minimum concave cost flows in certain networks Management Sci.,14(1968) 429–450.
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The revision of this paper was produced during the author’s stay partially supported by International Information Science Foundation at Sophia University, Tokyo.
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Thach, P.T. A decomposition method for the min concave cost flow problem with a staircase structure. Japan J. Appl. Math. 7, 103–120 (1990). https://doi.org/10.1007/BF03167893
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DOI: https://doi.org/10.1007/BF03167893