Sentence examples for properly efficient from inspiring English sources

This new definition of proper efficiency provide a new trade-off of a given properly efficient solution which can be new area of research.

This theorem shows that the new definition of properly efficient generalizes Geoffrion definition of properly efficient.

We call is a tightly properly efficient minimizer of (VP).

(ii If be a tightly properly efficient minimizer of (VP),.

The concept of (properly) efficient solutions are presented.

Therefore, is a tightly properly efficient solution of (VP).

If, then -efficient solution, weakly -efficient solution, and properly -efficient solution reduce to efficient solution, weakly efficient solution and properly efficient solution of problem (2.1).

We know that Henig' properly efficient solution equivalent to Benson properly efficient solution, when is a closed convex pointed cone(see [24]).

and there exists such that is a tightly properly efficient minimizer of the problem (UVP).

(ii) In [1], the cone characterizations of Henig' properly efficient solution were derived.

This means that ( x ¯ is a properly efficient solution in problem (MWDP).