From 33d26277b2602352eceb3d93733b1a8fc8bd18b3 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Thu, 20 Aug 2015 14:18:20 -0400 Subject: [PATCH] Update discrete_complementarity_set() docs. --- mjo/cone/cone.py | 20 +++++++++----------- 1 file changed, 9 insertions(+), 11 deletions(-) diff --git a/mjo/cone/cone.py b/mjo/cone/cone.py index 3c582e6..7374fcf 100644 --- a/mjo/cone/cone.py +++ b/mjo/cone/cone.py @@ -214,24 +214,22 @@ def _restrict_to_space(K, W): def discrete_complementarity_set(K): r""" - Compute the discrete complementarity set of this cone. + Compute a discrete complementarity set of this cone. - The complementarity set of a cone is the set of all orthogonal pairs - `(x,s)` such that `x` is in the cone, and `s` is in its dual. The - discrete complementarity set is a subset of the complementarity set - where `x` and `s` are required to be generators of their respective - cones. - - For polyhedral cones, the discrete complementarity set is always - finite. + A discrete complementarity set of `K` is the set of all orthogonal + pairs `(x,s)` such that `x \in G_{1}` and `s \in G_{2}` for some + generating sets `G_{1}` of `K` and `G_{2}` of its dual. Polyhedral + convex cones are input in terms of their generators, so "the" (this + particular) discrete complementarity set corresponds to ``G1 + == K.rays()`` and ``G2 == K.dual().rays()``. OUTPUT: A list of pairs `(x,s)` such that, * Both `x` and `s` are vectors (not rays). - * `x` is a generator of this cone. - * `s` is a generator of this cone's dual. + * `x` is one of ``K.rays()``. + * `s` is one of ``K.dual().rays()``. * `x` and `s` are orthogonal. REFERENCES: -- 2.44.2