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On Second-Order Necessary Conditions for Broken Extremals

Author

Listed:
  • Nikolai P. Osmolovskii

    (University of Technology and Humanities
    Systems Research Institute
    Moscow State University of Civil Engineering)

Abstract

We consider optimal control problems with initial–final state equality and inequality constraints and running mixed state-control equality constraints given by smooth functions. The mixed constraints satisfy the regularity assumption of linear independence of gradients with respect to the control. We present simple proofs of second-order necessary conditions for (extended) weak minimum for extremals with discontinuous controls in these problems.

Suggested Citation

  • Nikolai P. Osmolovskii, 2015. "On Second-Order Necessary Conditions for Broken Extremals," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 379-406, February.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:2:d:10.1007_s10957-014-0599-2
    DOI: 10.1007/s10957-014-0599-2
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    Cited by:

    1. Nikolai Pavlovich Osmolovskii, 2020. "Necessary Second-Order Conditions for a Strong Local Minimum in a Problem with Endpoint and Control Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 1-16, April.

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