2019/06/17 by Elimhan N. Mahmudov, Mahmudov, Elimhan N.
Computer Science · Engineering · Mathematics · #34A60 #49M25 #49N15 #90C46 #Advanced Optimization Algorithms Research #Aerospace Engineering and Control Systems #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1906.06872
openalex publication_date 2019/06/17 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
The paper deals with the optimal control problem described by second order\nevolution differential inclusions; to this end first we use an auxiliary\nproblem with second order discrete and discrete-approximate inclusions. Then\napplying infimal convolution concept of convex functions, step by step we\nconstruct the dual problems for discrete, discrete-approximate and differential\ninclusions and prove duality results. It seems that the Euler-Lagrange type\ninclusions are "duality relations" for both primary and dual problems and that\nthe dual problem for discrete-approximate problem make a bridge between them.\nFinally, relying to the method described within the framework of the idea of\nthis paper a dual problem can be obtained for any higher order differential\ninclusions. In this way relying to the described method for computation of the\nconjugate and support functions of discrete-approximate problems a Pascal\ntriangle with binomial coefficients, can be successfully used for any "higher\norder" calculations.\n