Mathematical Programming

, Volume 160, Issue 1–2, pp 115–147 | Cite as

Second order analysis of control-affine problems with scalar state constraint

Full Length Paper Series A


In this article we establish new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition.

Mathematics Subject Classification

49K15 49K27 



We wish to thank the anonymous referees for their bibliographical advices. This work was partially supported by the European Union under the 7th Framework Pro-gramme FP7-PEOPLE-2010-ITN Grant Agreement Number 264735-SADCO. The last stage of this research took place while the first author was holding a postdoctoral position at IMPA, Rio de Janeiro, with CAPES-Brazil funding.


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2016

Authors and Affiliations

  1. 1.EMAp/FGVRio de JaneiroBrazil
  2. 2.INRIA-Saclay and Centre de Mathématiques AppliquéesEcole PolytechniquePalaiseauFrance
  3. 3.Curtin UniversityMiriMalaysia

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