Duality for robust multi-dimensional vector variational control problem under invexity
This paper presents a multi-dimensional vector variational control problem wherein constraints are comprised of first order partial derivatives. As the optimization problems may contain uncertainties driven by measurement and manufacturing errors, erroneous information, irregularities, or perturbations, so the parameter’s randomness is assumed to be in the form of an uncertainty set. Firstly, the sufficient efficiency conditions are demonstrated for the problem under consideration. Then, the Wolfe type and Mond Weir type duals of the primal problem have been formulated. As in multi objective optimization models, attainment of efficient or weak efficient is the primary aim, thus the important robust duality theorems viz. weak, strong and strict converse duality theorems have been established under invexity conditions for Wolfe type dual. An example is also provided to illustrate the weak duality theorem. Thereafter, the duality results for Mond Weir type duals have been obtained under weaker invexity assumptions on involved functionals. This work extends the previously studied results on control problems and hence seeks application in diverse fields.
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