Stability of Discrete Approximations and Necessary Optimality Conditions for Delay-Differential Inclusions |
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Authors: | Boris S Mordukhovich Ruth Trubnik |
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Institution: | (1) Department of Mathematics, Wayne State University, Detroit, MI 48202, USA;(2) Department of Mathematical Sciences, Morris Brown College, Atlanta, GA 30314, USA |
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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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Keywords: | dynamic optimization delay-differential inclusions finite-difference perturbations stability variational analysis generalized differentiation necessary optimality conditions |
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