Parametric approach to multitime multiobjective fractional variational problems under \((F,\rho)\)-convexity. (English) Zbl 1348.90560
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 \((F,\rho)\)-convexity and generalized \((F,\rho)\)-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) \((F,\rho)\)-convexity.
MSC:
| 90C29 | Multi-objective and goal programming |
| 90C46 | Optimality conditions and duality in mathematical programming |
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