Journal of Global Optimization

, Volume 55, Issue 3, pp 559–577 | Cite as

A new necessary and sufficient global optimality condition for canonical DC problems

  • Qinghua Zhang


The paper proposes a new necessary and sufficient global optimality condition for canonical DC optimization problems. We analyze the rationale behind Tuy’s standard global optimality condition for canonical DC problems, which relies on the so-called regularity condition and thus can not deal with the widely existing non-regular instances. Then we show how to modify and generalize the standard condition to a new one that does not need regularity assumption, and prove that this new condition is equivalent to other known global optimality conditions. Finally, we show that the cutting plane method, when associated with the new optimality condition, could solve the non-regular canonical DC problems, which significantly enlarges the application of existing cutting plane (outer approximation) algorithms.


Global optimization DC programming Global optimality condition Cutting plane algorithms 


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© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina

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