Fenchel duality as well as Lagrangian duality arc developed in the vector optimization framework. Then existence of saddle points and conditions of weak optimality involving saddle points are discussed.
In multiple objective programming it is generally more convenient to study the efficient outcome instead of the efficient solution set. In general an approximation of this efficient outcome is obtained by solving a sequence of optimization problems. In this work we consider a special class of bicriteria optimization problems with linear fractional objectives and linear constraints. It is shown that the efficient outcome is the graph of a piecewise linear fractional curve in the plane, which can be easily computed. A finite algorithm is presented which generates this curve by simply considering some particular edges of the constraint polyhedron.