Parametric approach to multitime multiobjective fractional variational problems under (F,ρ)-convexity

• Published in: Optimal control applications & methods Vol. 37; no. 5; pp. 831 - 847
• Main Authors: Antczak, Tadeusz, Pitea, Ariana
• Format: Journal Article
• Language: English
• Published: Glasgow Blackwell Publishing Ltd 01.09.2016; Wiley Subscription Services, Inc
• Subjects: (F,ρ)‐convexity; duality; efficient solution; Functionals; Integrals; Mathematical programming; Multiple objective analysis; multitime multiobjective fractional variational problem; Optimal control; optimality; Optimization; parametric approach; Partial differential equations; Quotients; ρ)-convexity
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2192

Summary In this paper, we consider a multitime multiobjective fractional variational problem of minimizing a vector of quotients of path‐independent curvilinear integral functionals subject to certain partial differential equations and inequations. Using the so‐called parametric approach, we establish necessary and sufficient optimality conditions for the considered class of multitime multiobjective fractional variational problems under both (F,ρ)‐convexity and generalized (F,ρ)‐convexity. Further, the parametric multiobjective variational dual problem is formulated for the considered multitime multiobjective fractional variational problem, and several duality results are established under (generalized) (F,ρ)‐convexity. Copyright © 2015 John Wiley & Sons, Ltd.