Optimality Conditions and Total Dualities for Vector Optimization Problems
In this paper,by using the properties of subdifferential of vector func-tions,we introduce some new weaker constraint qualifications.By using those con-straint qualifications,optimality conditions for the vector optimization problem are established.Moreover,by using the properties of conjugate map,we define the La-grange,Fenchel-Lagrange and Total-Fenchel-Lagrange type dual problems for the vector optimization problem.Under these constraint qualifications,the total duality and the stable total duality between vector optimization problem and its three types of dual problems are established.Our results extend the corresponding results in the previous papers.
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