Econometrica: May, 1977, Volume 45, Issue 4

Necessary and Sufficient Conditions for a Pareto Optimum in Convex Programming

https://doi.org/0012-9682(197705)45:4<811:NASCFA>2.0.CO;2-U
p. 811-820

A. Ben-Israel, A. Ben-Tal, A. Charnes

Necessary and sufficient conditions for Pareto optimality are derived for problems involving convex criteria and convex constraints. For a wide class of convex functions, the characterization of Pareto optimality is given in terms of systems of linear programs, which, under suitable regularization conditions, reduce to a single linear program. The consideration of a system of linear programs and their duals leads naturally to a system of partial prices associated with a Pareto optimum.