Schur-convex function: Difference between revisions

Revision as of 02:56, 20 September 2012

Revision as of 03:02, 20 September 2012

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* The [[Rényi entropy]] funtion is also Schur-concave.

* <math> \sum_{i=1}^d{x_i^k},k \ge 1 </math> is Schur-convex.

* The function $<math> f(x) = \prod_{i=1}^n x_i </math> is Schur-concave, when we assume all $<math> x_i > 0$ </math>. In the same way, all the

[[Elementary symmetric polynomial|Elementary symmetric function]]s are Schur-convex, when $<math> x_i > 0$ </math>.

* A natural interpretation of [[majorization]] is that if <math> x \succ y </math> then

[[Category:Convex analysis]]