Relaxation in nonconvex optimal control problems with subdifferential operators |
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Authors: | A A Tolstonogov |
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Institution: | (1) Institute of System Dynamics and Control Theory, Siberian Department of the Russian Academy of Sciences, Russia |
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Abstract: | We consider the minimization problem of an integral functional in a separable Hilbert space with integrand not convex in the
control defined on solutions of the control system described by nonlinear evolutionary equations with mixed nonconvex constraints.
The evolutionary operator of the system is the subdifferential of a proper, convex, lower semicontinuous function depending
on time.
Along with the initial problem, the author considers the relaxed problem with the convexicated control constraint and the
integrand convexicated with respect to the control.
Under sufficiently general assumptions, it is proved that the relaxed problem has an optimal solution, and for any optimal
solution, there exists a minimizing sequence of the initial problem converging to the optimal solution with respect to trajectories
and the functional. An example of a controlled parabolic variational inequality with obstacle is considered in detail.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 26, Nonlinear
Dynamics, 2005. |
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Keywords: | |
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