Monotonic optimization is concerned with optimization problems dealing with multivariate monotonic functions and differences of monotonic functions. For the study of this class of problems a general framework (Tuy, 2000a) has been earlier developed where a key role was given to a separation property of solution sets of monotonic inequalities similar to the separation property of convex sets. In the present paper the separation cut is combined with other kinds of cuts, called reduction cuts, to further exploit the monotonic structure. Branch and cuts algorithms based on an exhaustive rectangular partition and a systematic use of cuts have proved to be much more efficient than the original polyblock and copolyblock outer approximation algorithms.
- Feasible Solution
- Global Optimization
- Separation Property
- Outer Approximation
- Approximate Optimal Solution
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Tuy, H., Al-Khayyal, F., Thach, P.T. (2005). Monotonic Optimization: Branch and Cut Methods. In: Audet, C., Hansen, P., Savard, G. (eds) Essays and Surveys in Global Optimization. Springer, Boston, MA. https://doi.org/10.1007/0-387-25570-2_2
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