Saddle points and duality in multi-objective programming
Tetsuzo Tanino · International Journal of Systems Science · 1982
This paper deals with saddle points of vector-valued functions and duality in multi-objective programming. First, saddle points for vector-valued functions are defined as a generalization of those for scalar-valued functions. Some properties of them are derived. Secondly, it. is shown that multi-objective programming problems are closely connected with vector-valued lagrangians. Solutions to multi-objective programming problems and corresponding multiplier vectors are saddle points of vector-valued lagrangians. Multiplier vectors are also sub-gradients for perturbation maps. Finally, there exists a corresponding multiplier vector, which is a solution to the dual problem, for each solution to some class of primal problems (stable problems).