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Regularity Properties of Optimal Controls with Application to Discrete Approximation

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  • U. Felgenhauer

    (Brandenburgische Technische Universität)

Abstract

This paper is directed to the analysis of regularity properties of optimal solutions for a nonlinear control problem with convex control constraints. Since the problem formulation is given typically in L ∞-terms, we introduce first the essential limit set as a tool for the local investigation of L ∞-functions. Under second-order conditions of the coercivity type on the solution, a structural result is obtained characterizing the local behavior of the optimal control by means of Lipschitz continuous functions. Further, the consequences for certain discrete approximations are discussed; for uniquely solvable problems, we show the Lipschitz continuity of the optimal control.

Suggested Citation

  • U. Felgenhauer, 1999. "Regularity Properties of Optimal Controls with Application to Discrete Approximation," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 97-110, July.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:1:d:10.1023_a:1021842412255
    DOI: 10.1023/A:1021842412255
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
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    Cited by:

    1. U. Felgenhauer, 2001. "Weak and Strong Optimality Conditions for Constrained Control Problems with Discontinuous Control," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 361-387, August.

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