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New optimality conditions for nonsmooth control problems

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  • Valeriano Oliveira
  • Geraldo Silva

Abstract

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every MP-process is optimal necessarily obey our first optimality condition. The second condition is more natural, but it is only applicable to normal problems and the converse holds just for smooth problems. Nevertheless, it is proved that for the class of normal smooth optimal control problems the two conditions are equivalent. Some examples illustrating the features of these sufficient concepts are presented. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Valeriano Oliveira & Geraldo Silva, 2013. "New optimality conditions for nonsmooth control problems," Journal of Global Optimization, Springer, vol. 57(4), pages 1465-1484, December.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:4:p:1465-1484
    DOI: 10.1007/s10898-012-0003-4
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    4. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    5. A. J. V. Brandão & M. A. Rojas-Medar & G. N. Silva, 1999. "Optimally Conditions for Pareto Nonsmooth Nonconvex Programming in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 65-73, October.
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