Abstract
We consider a global optimization problem of minimizing a linear function subject to p linear multiplicative constraints as well as ordinary linear constraints. We show that this problem can reduce to a 2p-dimensional reverse convex program, and present an algorithm for solving the resulting problem. Our algorithm converges to a globally optimal solution and yields an ∈-approximate solution in finite time for any ∈ > 0. We also report some results of computational experiment.
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Kuno, T., Konno, H. & Irie, A. A Deterministic Approach to Linear Programs with Several Additional Multiplicative Constraints. Computational Optimization and Applications 14, 347–366 (1999). https://doi.org/10.1023/A:1026404623838
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DOI: https://doi.org/10.1023/A:1026404623838