M. Iri, Network Flow, Transportation and Scheduling--Theory and Al- gorithms, Academic Press, New York, 1969.  Home/Search   Document Not in Database   Summary   Related Articles

....Japan, shiouradais. is. t ohoku. ac. jp. I Introduction In recent years, combinatorial optimization problems with nonlinear objective functions have been dealt with, and extensive studies have been done for revealing the well solved structure in nonlinear combinatorial opti mization problems [2, 4, 9, 10, 11, 23, 15, 16]. The concepts of M convexity and L convexity, introduced by Murota [12, 13, 15, 16] for functions on the integer lattice, extract combinatorial structures in well solved nonlinear combinatorial optimization problems; subsequently, their variants called M convexity and Lb convexity were ....

....by a function g: R T defined as g(p) inf ga(l(a) a) Si(a) a C A) if(v) p(v) v T) 7,P aEA for p R T. It cem be shown that both f and g re closed proper convex if f(xo) nd g(Po) re finite for some x0 R T emd P0 R T, which is a direct extension of the results in Iri [9] emd Rocka ellr [23] for the case of ITI = 2. These functions, however, re equipped with different combinatorial structures; f is M convex ad g is L convex. See [20, Th. 2.10] 3 M convex Functions M convex sets emd positively homogeneous M convex functions constitute importemt subclasses of ....

M. Iri, Network Flow, Transportation and Scheduling--Theory and Al- gorithms, Academic Press, New York, 1969.

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