## A finite branch-and-bound algorithm for linear multiplicative programming.(English)Zbl 0983.90075

Summary: On the basis of Soland’s rectangular branch and bound, we develop an algorithm for minimizing a product of $$p$$ $$(\geq 2)$$ 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.

### MSC:

 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut 90C05 Linear programming
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