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Multiobjective Linear Programming

In: Mathematical Optimization and Economic Analysis

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  • Mikuláš Luptáčik

    (Vienna University of Economics and Business Administration)

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.

Suggested Citation

  • Mikuláš Luptáčik, 2010. "Multiobjective Linear Programming," Springer Optimization and Its Applications, in: Mathematical Optimization and Economic Analysis, chapter 8, pages 243-269, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-89552-9_8
    DOI: 10.1007/978-0-387-89552-9_8
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