v2009.01.01 - Convex Optimization

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R m×n
Euclidean vector space of m by n dimensional real matrices
× Cartesian product. R m×n−m = ∆ R m×(n−m)
[ ] R
m
R n R m × R n = R m+n
C n or C n×n
Euclidean complex vector space of respective dimension n and n×n
R n + or R n×n
+ nonnegative orthant in Euclidean vector space of respective dimension
n and n×n
R n −
or R n×n
−
S n
S n⊥
S n +
int S n +
S n +(ρ)
EDM N
√
EDM
N
PSD
SDP
SVD
SNR
nonpositive orthant in Euclidean vector space of respective dimension
n and n×n
subspace comprising all (real) symmetric n×n matrices,
the symmetric matrix subspace
orthogonal complement of S n in R n×n , the antisymmetric matrices
convex cone comprising all (real) symmetric positive semidefinite n×n
matrices, the positive semidefinite cone
interior of convex cone comprising all (real) symmetric positive
semidefinite n×n matrices; id est, positive definite matrices
convex set of all positive semidefinite n×n matrices whose rank equals
or exceeds ρ
cone of N ×N Euclidean distance matrices in the symmetric hollow
subspace
nonconvex cone of N ×N Euclidean absolute distance matrices in the
symmetric hollow subspace
positive semidefinite
semidefinite program
singular value decomposition
signal to noise ratio