2020/09/16 by Elimhan N. Mahmudov, Mahmudov, Elimhan N.
Computer Science · Mathematics · #Contact Mechanics and Variational Inequalities #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2009.07721
openalex publication_date 2020/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper studies optimal control problem described by higher order evolution\ndifferential inclusions (DFIs) with endpoint and state constraints. In the term\nof Euler-Lagrange type inclusion is derived sufficient condition of optimality\nfor higher order DFIs. It is shown that the adjoint inclusion for the first\norder DFIs, defined in terms of locally adjoint mapping, coincides with the\nclassical Euler-Lagrange inclusion. Then a duality theorem is proved, which\nshows that Euler-Lagrange inclusions are "duality relations" for both problems.\nAt the end of the paper duality problems for third order linear and fourth\norder polyhedral DFIs are considered.\n