From the Ideas of Edgeworth and Pareto in Exchange Economy to Multi-Objective Mathematical Programming

Volume 2, Issue 2, April 2017     |     PP. 15-27      |     PDF (321 K)    |     Pub. Date: April 25, 2017
DOI:    326 Downloads     5065 Views  

Author(s)

Zdravko Dimitrov Slavov, Varna Free University, Varna, Bulgaria
Christina Slavova Evans, The George Washington University, Washington DC, USA

Abstract
In this paper we consider the first general theories of multi-objective mathematical programming. They stem from optimization techniques in economics and are attributed to the economists Francis Edgeworth and Vilfredo Pareto. We will focus our attention on these ideas from a mathematical point of view.

Keywords
optimization, multi-objective mathematical programming, Edgeworth-box, Pareto-optimal, equilibrium.

Cite this paper
Zdravko Dimitrov Slavov, Christina Slavova Evans, From the Ideas of Edgeworth and Pareto in Exchange Economy to Multi-Objective Mathematical Programming , SCIREA Journal of Mathematics. Volume 2, Issue 2, April 2017 | PP. 15-27.

References

[ 1 ] K. Arrow, Social Choice and Individual Values, Cowles Commission for Research in Economics Monograph N:12, John Wiley and Sons, 1951.
[ 2 ] M. Ehrgott, X. Gandibleux, Multi-criteria Optimization: State of the Art Annotated Bibliographic Surveys. Kluwer Academic Press, 2002.
[ 3 ] M. Ehrgott, Multi-criteria Optimization. Springer, 2005.
[ 4 ] M. Ehrgott, Vilfredo Pareto and multi-objective optimization. Documenta Mathematica, Extra volume: Optimization Stories, 447-453, 2012.
[ 5 ] B. Ellickson, Competitive Equilibrium: Theory and Applications, Cambridge University Press, 1997.
[ 6 ] A. Feldman, R. Serrano, Welfare Economics and Social Choice Theory, Springer, 2006.
[ 7 ] J. Jahn, Vector Optimization: Theory, Applications, and Extensions. Springer, 2004.
[ 8 ] T. Koopmans, Analysis of Production as an efficient Combination of Activities, in T. Koopmans, editor, Cowles Commission for Research in Economics Monograph N:13, John Wiley and Sons, 1951, 33-97.
[ 9 ] D. Luc, Theory of Vector Optimization. Springer, 1989,
[ 10 ] H. Kuhn, A. Tucker, Nonlinear programming, in J. Neyman, editor, Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, CA, 1951, 481-492.
[ 11 ] M. Luptacik, Mathematical Optimization and Economic Analysis, Springer, 2010.
[ 12 ] Z. Slavov, Structure of the Pareto optimality set with fixed total resources and consumption sets, Applied Mathematics and Computation 154 (2004), 75-81.
[ 13 ] R. Steuer, Multiple Criteria Optimization: Theory, Computation and Application, John Wiley and Sons, 1986.