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Infimal convolution and duality in convex optimal control problems with second order evolution differential inclusions. (English) Zbl 1476.49029

Summary: The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying infimal convolution concept of convex functions, step by step we construct the dual problems for discrete, discrete-approximate and differential inclusions and prove duality results. It seems that the Euler-Lagrange type inclusions are “duality relations” for both primary and dual problems and that the dual problem for discrete-approximate problem make a bridge between them. At the end of the paper duality in problems with second order linear discrete and continuous models and model of control problem with polyhedral DFIs are considered.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
49J52 Nonsmooth analysis
49N15 Duality theory (optimization)
34A60 Ordinary differential inclusions
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