v2006.03.09 - Convex Optimization

615EDM NPSDSDPEDMS n 1S n hS n⊥hS n ccone of N × N Euclidean distance matrices in the symmetric hollowsubspacepositive semidefinitesemidefinite programEuclidean distance matrixsubspace comprising all symmetric n×n matrices having all zeros infirst row and column (1565)subspace comprising all symmetric hollow n×n matrices (0 maindiagonal), the symmetric hollow subspace (55)orthogonal complement of S n h in Sn (56), the set of all diagonal matricessubspace comprising all geometrically centered symmetric n×nmatrices; geometric center subspace S N ∆c = {Y ∈ S N | Y 1=0} (1561)S n⊥c orthogonal complement of S n c in S n (1563)R 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 ⊥K M+K MK ∗ λδH∂Hnormal conemonotone nonnegative conemonotone conecone of majorizationhalfspacehyperplane; id est, partial boundary of halfspace