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Asymptotic behaviour of the minima to a class of optimization problems for differential inclusions

  • Z. Denkowski
  • V. Staicu
Contributed Papers

Abstract

Denoting byS k k ) the set of solutions of the Cauchy problem\(\dot x \in F_k (t,x),x(0) = \xi _k \), forkN∪{∞}, we prove that, under appropriate assumptions, the sequence {S k k )} k ∈ N converges toS(∈) in the Kuratowski sense as well as in the Mosco sense. This result together with some facts from Γ-convergence theory are used to prove a result concerning the existence and the asymptotic behavior of the minima to the optimization problem
$$\min \int_0^T {[g_k (t,x(t)) + h_k (t,\dot x(t))]} dt + \psi _k (\xi ),x \in S_k (\xi ),\xi \in K$$
withK a compact subset ofR n .

Key Words

Optimization problems functionals of Bolza type differential inclusions Γ-convergence Kuratowski convergence Mosco convergence 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Z. Denkowski
    • 1
  • V. Staicu
    • 2
  1. 1.Institute for Information SciencesJagellonian UniversityKrakowPoland
  2. 2.Mathematics SectionInternational Centre for Theoretical PhysicsTriesteItaly

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