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No-gap second-order optimality conditions for optimal control problems with a single state constraint and control

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Abstract

The paper deals with optimal control problems with only one control variable and one state constraint, of arbitrary order. We consider the case of finitely many boundary arcs and touch times. We obtain a no-gap theory of second-order conditions, allowing to characterize second-order quadratic growth.

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Authors and Affiliations

  1. CMAP, Ecole Polytechnique, INRIA Futurs, Route de Saclay, 91128, Palaiseau, France

    J. Frédéric Bonnans & Audrey Hermant

Authors
  1. J. Frédéric Bonnans
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  2. Audrey Hermant
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Correspondence to J. Frédéric Bonnans.

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Dedicated to Professor S.M. Robinson on the occasion of his 65th birthday.

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Frédéric Bonnans, J., Hermant, A. No-gap second-order optimality conditions for optimal control problems with a single state constraint and control. Math. Program. 117, 21–50 (2009). https://doi.org/10.1007/s10107-007-0167-8

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  • DOI: https://doi.org/10.1007/s10107-007-0167-8

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