2010/07/20 by Ewa Girejko, Agnieszka B. Malinowska, Delfim F. M. Torres · 12 citations
Computer Science · Mathematics · #Applied mathematics #Combinatorics #Fixed Point Theorems Analysis #Isoperimetric inequality #Mathematical optimization #Mathematics #Multi-objective optimization #Nabla symbol #Nonlinear Differential Equations Analysis #Optimal control #Optimization and Variational Analysis #Pareto optimal #Physics #math.OC #msc:26E70 #msc:34N05 #msc:49K05
paper · pdf · doi:10.1177/1077546310381271
published in Journal of Vibration and Control 17(11), 1634-1643 (SAGE Publishing) · Preprint version of an article submitted 28-Nov-2009; revised 02-Jul-2010; accepted 20-Jul-2010; for publication in Journal of Vibration and Control
arxiv created 2010/07/20 · openalex publication_date 2010/11/22 · arxiv updated 2011/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and previous results in the literature are obtained as particular cases. As an application of the results of the paper we give necessary and sufficient Pareto optimality conditions for delta-nabla bi-objective optimal control problems.