Abstract
For solving global optimization problems with nonconvex feasible sets existing methods compute an approximate optimal solution which is not guaranteed to be close, within a given tolerance, to the actual optimal solution, nor even to be feasible. To overcome these limitations, a robust solution approach is proposed that can be applied to a wide class of problems called \({{\mathcal {D}(\mathcal {C})}}\)-optimization problems. DC optimization and monotonic optimization are particular cases of \({{\mathcal {D}(\mathcal {C})}}\)-optimization, so this class includes virtually every nonconvex global optimization problem of interest. The approach is a refinement and extension of an earlier version proposed for dc and monotonic optimization.
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Tuy, H. \({{\mathcal {D}(\mathcal {C})}}\)-optimization and robust global optimization. J Glob Optim 47, 485–501 (2010). https://doi.org/10.1007/s10898-009-9475-2
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DOI: https://doi.org/10.1007/s10898-009-9475-2
Keywords
- Nonconvex global optimization
- Approximate optimal solution
- Robust approach
- Essential optimal solution
- dc optimization
- dm (monotonic) optimization
- \({{\mathcal {D}(\mathcal {C})}}\)-optimization
- Successive Incumbent Transcending Algorithm