Optimization of higher order differential inclusions with initial value problem

Mahmudov E. N.

APPLICABLE ANALYSIS, vol.96, no.7, pp.1215-1228, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 96 Issue: 7
  • Publication Date: 2017
  • Doi Number: 10.1080/00036811.2016.1182993
  • Title of Journal : APPLICABLE ANALYSIS
  • Page Numbers: pp.1215-1228


This paper concerns the sufficient conditions of optimality for initial value problem with higher order differential inclusions (HODIs) and free endpoint constraints. Formulation of the transversality conditions plays a substantial role in the next investigations without which hardly any necessary or sufficient conditions would be obtained. In terms of Euler-Lagrange and Hamiltonian forms the sufficient conditions of optimality both for convex and "non-convex" HODIs are based on the apparatus of locally adjoint mappings. Moreover, by applying the main result to a Bolza problem described by a polynomial differential operator with constant coefficients in terms of the adjoint differential operator the sufficient condition of optimality is obtained.