Minimizing a linear multiplicative-type function under network flow constraints

Authors:
Takahito Kuno;Takahiro Utsunomiya
Affiliations:
Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan;Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, Ibaraki 305, Japan
Venue:
Operations Research Letters
Year:
1997

Citing 6
Cited 0

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Minimum concave-cost network flow problems: applications, complexity, and algorithms

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Linear multiplicative programming

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Strongly polynomial time algorithms for certain concave minimization problems on networks

Operations Research Letters

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Abstract

In this paper, we consider a special class of nonconvex network flow problems, whose objective function is a product of two affine functions. This problem arises when one tries to send as much flow as possible in an ordinary two-terminal network at the minimum possible cost. We will show that a primal-dual algorithm can generate a globally optimal solution in pseudo-polynomial time and a globally @e-optimal solution in polynomial time.