Proper efficiency principles and duality models for a class of continuous-time multiobjective fractional programming problems with operator constraints

Abstract

Necessary and sufficient saddle-point- and stationary-point-type proper efficiency conditions are established for a class of continuous-time multiobjective fractional programming problems with convex operator inequality and affine operator equality constraints. Subsequently, the form and contents of these proper efficiency results are utilized for constracting a Lagrangian-type, two parametric, and four semiparametric duality models, and for proving appropriate duality theorems. These proper efficiency and duality results contain, as special cases, similar results for continuous-time programming problems with nonfractional multiple, single fractional, and conventional objective functions, which are patricular cases of the principal problem studied in this paper.