v2007.09.13 - Convex Optimization

680 APPENDIX G. NOTATION AND A FEW DEFINITIONSR m×ncsubspace comprising all geometrically centered m×n matricesX ⊥ basis N(X T )x ⊥ N(x T ) , {y | x T y = 0}R(P ) ⊥ N(P T )R ⊥ orthogonal complement of R⊆ R n ; R ⊥ ={y ∆ ∈ R n | 〈x,y〉=0 ∀x∈ R}K ⊥Knormal coneconeK ∗dual coneK ◦ polar cone; K ∗ = −K ◦K M+K MK λK ∗ λδHH −H +∂H∂H∂H −∂H +monotone nonnegative conemonotone conespectral conecone of majorizationhalfspacehalfspace described using an outward-normal (86) to the hyperplanepartially bounding ithalfspace described using an inward-normal (87) to the hyperplanepartially bounding ithyperplane; id est, partial boundary of halfspacesupporting hyperplanea supporting hyperplane having outward-normal with respect to set itsupportsa supporting hyperplane having inward-normal with respect to set itsupports