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Computational Optimization and Applications

, Volume 20, Issue 2, pp 119–135 | Cite as

A Finite Branch-and-Bound Algorithm for Linear Multiplicative Programming

  • Takahito Kuno
Article

Abstract

On the basis of Soland's rectangular branch-and-bound, we develop an algorithm for minimizing a product of p (≥2) affine functions over a polytope. To tighten the lower bound on the value of each subproblem, we install a second-stage bounding procedure, which requires O(p) additional time in each iteration but remarkably reduces the number of branching operations. Computational results indicate that the algorithm is practical if p is less than 15, both in finding an exact optimal solution and an approximate solution.

global optimization nonconvex optimization linear multiplicative programming branch-and-bound algorithm continuous knapsack problem 

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© Kluwer Academic Publishers 2001

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  • Takahito Kuno

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