Sufficiency and duality of Gteaux differentiable multi-objective optimization in topological vector spaces

In this paper,the authors deal with the sufficiency and duality for a multi-objective optimization problem where all functions involved are defined on locally convex Hausdorff topological vector spaces.Several classes of generalized type-Ⅰmappings are introduced for Gteaux differentiable mappings between locally convex Hausdorff topological vector spaces.Based upon these generalized type-Ⅰmappings,they obtain a few sufficient optimality conditions and prove some results on duality.