v2007.09.17 - Convex Optimization

681R n −or R n×n−S nS n⊥S n +int S n +S n +(ρ)EDM N√EDMNPSDSDPSVDEDMS n 1S n hS n⊥hS n cnonpositive orthant in Euclidean vector space of respective dimensionn and n×nsubspace comprising all (real) symmetric n×n matrices,the symmetric matrix subspaceorthogonal complement of S n in R n×n , the antisymmetric matricesconvex cone comprising all (real) symmetric positive semidefinite n×nmatrices, the positive semidefinite coneinterior of convex cone comprising all (real) symmetric positivesemidefinite n×n matrices; id est, positive definite matricesconvex set of all positive semidefinite n×n matrices whose rank equalsor exceeds ρcone of N ×N Euclidean distance matrices in the symmetric hollowsubspacenonconvex cone of N ×N Euclidean absolute distance matrices in thesymmetric hollow subspacepositive semidefinitesemidefinite programsingular value decompositionEuclidean distance matrixsubspace comprising all symmetric n×n matrices having all zeros infirst row and column (1770)subspace comprising all symmetric hollow n×n matrices (0 maindiagonal), the symmetric hollow subspace (56)orthogonal complement of S n h in Sn (57), 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} (1766)S n⊥c orthogonal complement of S n c in S n (1768)