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.
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Mordukhovich, B.S., Trubnik, R. Stability of Discrete Approximations and Necessary Optimality Conditions for Delay-Differential Inclusions. Annals of Operations Research 101, 149–170 (2001). https://doi.org/10.1023/A:1010968423112
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DOI: https://doi.org/10.1023/A:1010968423112