Sufficiency and duality for complex multiobjective fractional programming involving cone constraints

This paper aims to investigate sufficiency and duality of a multiobjective fractional programming problem in complex space. The functions involved are ratio of two functions and the constraints are defined in cones. Firstly, the result asserting the ratio invexity in complex space has been discussed and the same has been supported by examples. This is followed by sufficiency conditions for the problem under consideration. Further, to illustrate this result, an example has been provided. It is worth mentioning that an efficient solution of the problem considered in the example is also obtained using Multiobjective Genetic Algorithm (MOGA) which alongwith the sufficiency conditions become more reliable. In the literature, various forms of duals for a fractional programming problem have been studied. Here, we have formulated a Bector type dual corresponding to a fractional programming problem in complex space and important duality results relating the solutions of primal and dual problems have been proved under generalized convexity assumptions which widen its application in diverse fields.