Abstract
In this paper, a new class of ( C , G f ) -invex functions introduce and give nontrivial numerical examples which justify exist such type of functions. Also, we construct generalized convexity definitions (such as, ( F , G f ) -invexity, C-convex etc.). We consider Mond–Weir type fractional symmetric dual programs and derive duality results under ( C , G f ) -invexity assumptions. Our results generalize several known results in the literature.
Highlights
The goal of optimization is to find the best value for each variable in order to achieve satisfactory performance
In [3], Antczak extended the above notion by defining a vector valued G f -invex function and proved necessary and sufficient optimality conditions for a multiobjective nonlinear programming problem
We considered a pair of multiobjective Mond–Weir type symmetric fractional primal-dual problems
Summary
The goal of optimization is to find the best value for each variable in order to achieve satisfactory performance. In most real life problems, decisions are made taking into account several conflicting criteria, rather than by optimizing a single objective. Such a problem is called multiobjective programming. In 1981, Hanson [1] introduced the concept of invexity which is an extension of differentiable convex function and proved the sufficiency of Kuhn-Tucker conditions. In [3], Antczak extended the above notion by defining a vector valued G f -invex function and proved necessary and sufficient optimality conditions for a multiobjective nonlinear programming problem. Ferrara and Stefaneseu [8] used the (φ, ρ)-invexity to discuss the optimality conditions and duality results for multiobjective programming problem. Under the (C, G f )-invexity assumptions, we derive duality results
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