picos.expressions.exp_nucnorm¶
Implements NuclearNorm
.
Classes
- class picos.expressions.exp_nucnorm.NuclearNorm(x)[source]¶
Bases:
Expression
The nuclear norm of a matrix.
This class can represent the nuclear norm of a matrix-affine expression (real- or complex valued). The nuclear norm is convex, so we can form expressions of the form
NuclearNorm(X) <= t
which are typically reformulated as LMIs that can be handled by SDP solvers.- Definition
If the normed expression is a matrix
, then its nuclear norm is
where the
denote the singular values of a
, and
denotes the adjoint matrix of
(i.e., the transposed matrix
if
is real-valued).
Special cases:
If
is scalar, then
reduces to the the absolute value (or modulus)
.
If
is scalar, then
coincides with the Euclidean norm of
.
- __init__(x)[source]¶
Construct a
NuclearNorm
.- Parameters
x (ComplexAffineExpression) – The affine expression to take the norm of.
- property x¶
Real expression whose norm equals that of the original expression.