Schur-convex function: Difference between revisions

Revision as of 05:39, 1 December 2013

Revision as of 05:42, 1 December 2013

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If <math>f</math> is Schur-convex and all first partial derivatives exist, then the following holds, where <math> f_{(i)}(x) </math> denotes the partial derivative with respect to <math> x_i </math>:

:<math> (x_ix_1 - x_jx_2)(f_{(i1)}(x) - f_{(j2)}(x)) \ge 0

</math> for all <math> x </math>. Since <math> f </math> is a symmetric function, the above condition implies all the similar conditions for the remaining indexes!