05657102

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05657102 Pitea, Ariana Udri\c ste, Constantin Mititelu, \c Stefan PDI\&PDE-constrained optimization problems with curvilinear functional quotients as objective vectors. Balkan J. Geom. Appl. 14, No. 2, 65-78 (2009). 2009 Balkan Society of Geometers, Bucharest; Geometry Balkan Press, Bucharest EN PDI\&PDE constraints multi-objective fractional variational problem Pareto optimality quasiinvexity duality Summary: We introduce and perform a study on the multitime multi-objective fractional variational problem of minimizing a vector of quotients of path independent curvilinear integral functionals (MFP) subject to certain Partial Differential Equations (PDE) and/or Partial Differential Inequations (PDI), using a geometrical language. The paper is organized as follows: \S1 formulates a PDI\&PDE-constrained optimization problem. \S2 states and proves necessary conditions for the optimality of the problem of minimizing a vector of path independent curvilinear integral functionals constrained by PDIs and PDEs. \S3 analyzes necessary efficiency conditions for the problem (MFP), and \S4 studies different types of dualities.