2015/04/20 by Amar Debbouche, Juan J. Nieto, Delfim F. M. Torres · 1 citation
Engineering · Mathematics · #Differential Equations and Boundary Problems #Minification #Nonlinear Differential Equations Analysis #Nonlinear system #Optimal control #Regular polygon #Relaxation (psychology) #Sobolev space #Soil, Finite Element Methods #Theory of computation #Type (biology) #math.CA #math.OC #msc:26A33 #msc:34B10 #msc:49J15 #msc:49J45
paper · pdf · doi:10.1007/s10957-015-0743-7
published as J. Optim. Theory Appl. 174 (2017), no. 1, 7--31 · This is a preprint of a paper whose final and definite form will be published in Journal of Optimization Theory and Applications, ISSN 0022-3239 (print), ISSN 1573-2878 (electronic). Submitted: 26-Dec-2014; Revised: 14-Apr-2015; Accepted: 19-Apr-2015
arxiv created 2015/04/20 · openalex publication_date 2015/04/29 · openalex created_date 2016/06/24 · arxiv updated 2017/07/21 · openalex updated_date 2026/08/05
We introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the minimization problem of multi-integral functionals, with integrands that are not convex in the controls, of control systems with mixed nonconvex constraints on the controls. We prove, under appropriate conditions, that the relaxation problem admits optimal solutions. Furthermore, we show that those optimal solutions are in fact limits of minimizing sequences of systems with respect to the trajectory, multi-controls, and the functional in suitable topologies.