Research Of Some Problems In Nonsmooth Vector Optimization

In the thesis, the nonsmooth vector optimization problems with inequality constraints in real Banach space are studied. First, the necessary optimality conditions are presented through various cones. Then, by introducing upper and lower directional derivatives and generalized Minty type vector variational inequality, the optimality conditions of the problem (VP) are studied. Finally, the generalized constraint qualifications are proposed and Kuhn-Tucker type necessary optimality conditions, the generalized dual models and the stability are discussed again.