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Stability of Discrete Approximations and Necessary Optimality Conditions for Delay-Differential Inclusions

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  • Boris Mordukhovich
  • Ruth Trubnik

Abstract

This paper is devoted to the study of optimization problems for dynamical systems governed by constrained delay-differential inclusions with generally nonsmooth and nonconvex data. We provide a variational analysis of the dynamic optimization problems based on their data perturbations that involve finite-difference approximations of time-derivatives matched with the corresponding perturbations of endpoint constraints. The key issue of such an analysis is the justification of an appropriate strong stability of optimal solutions under finite-dimensional discrete approximations. We establish the required pointwise convergence of optimal solutions and obtain necessary optimality conditions for delay-differential inclusions in intrinsic Euler–Lagrange and Hamiltonian forms involving nonconvex-valued subdifferentials and coderivatives of the initial data. Copyright Kluwer Academic Publishers 2001

Suggested Citation

  • Boris Mordukhovich & Ruth Trubnik, 2001. "Stability of Discrete Approximations and Necessary Optimality Conditions for Delay-Differential Inclusions," Annals of Operations Research, Springer, vol. 101(1), pages 149-170, January.
    • Handle: RePEc:spr:annopr:v:101:y:2001:i:1:p:149-170:10.1023/a:1010968423112
    DOI: 10.1023/A:1010968423112
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