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**Outcome-space cutting-plane algorithm for linear multiplicative programming.**
*(English)*
Zbl 0962.90024

Summary: This article presents an outcome-space pure cutting-plane algorithm for globally solving the linear multiplicative programming problem. The framework of the algorithm is taken from a pure cutting-plane decision set-based method developed by Horst and Tuy for solving concave minimization problems. By adapting this method to an outcome-space reformulation of the linear multiplicative programming problem, rather than applying directly the method to the original decision-set formulation, it is expected that considerable computational savings can be obtained. Also, we show how additional computational benefits might be obtained by implementing the new algorithm appropriately. To illustrate the new algorithm, we apply it to the solution of a sample problem.

### MSC:

90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |

90C57 | Polyhedral combinatorics, branch-and-bound, branch-and-cut |

### Keywords:

global optimization; multiplicative programming; cutting plane; nonconvex programming; outcome space; extreme-point search
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\textit{H. P. Benson} and \textit{G. M. Boger}, J. Optim. Theory Appl. 104, No. 2, 301--322 (2000; Zbl 0962.90024)

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### References:

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