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Journal of Global Optimization

, Volume 47, Issue 3, pp 485–501 | Cite as

\({{\mathcal {D}(\mathcal {C})}}\)-optimization and robust global optimization

  • Hoang TuyEmail author
Article

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.

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 

AMS Subjcet Classfication

90C26 90C30 90C31 90C57 49K40 65K05 

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Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  1. 1.Institute of MathematicsHanoiVietnam

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