Multiobjective linear programming

Abstract

As in single-objective mathematical programming, the most developed part of multiobjective optimization-from the theoretical as well as the applications point of view-is multiobjective linear programming. In 1951, Gale, Kuhn, and Tucker [7] considered a pair of general matrix linear programming problems, i.e., a linear programming problem with a matrix-valued linear objective function, and established some theorems of existence and duality. With matrix linear programming problems containing linear programming problems with a vector-valued as well as a scalarvalued objective function as special cases, the developed theory comprises the respective theoretical framework for vector linear programming problems as well as for ordinary linear programming problems.