Expressions¶
CVXPY represents mathematical objects as expression trees. An expression
tree is a collection of mathematical expressions linked together by one or more
atoms. Expression trees are encoded as instances of the
Expression
class, and each
Leaf
in a tree is a
Variable
,
Parameter
, or
Constant
.
Expression¶

class
cvxpy.expressions.expression.
Expression
[source]¶ Bases:
cvxpy.utilities.canonical.Canonical
A mathematical expression in a convex optimization problem.
Overloads many operators to allow for convenient creation of compound expressions (e.g., the sum of two expressions) and constraints.

property
T
¶ The transpose of the expression.
 Type

__pow__
(power)[source]¶ Raise expression to a power.
 Parameters
power (
float
) – The power to which to raise the expression. Returns
The expression raised to
power
. Return type

property
curvature
¶ The curvature of the expression.
 Type
str

abstract property
domain
¶ The constraints describing the closure of the region where the expression is finite.
 Type
list

abstract property
grad
¶ Gives the (sub/super)gradient of the expression w.r.t. each variable.
Matrix expressions are vectorized, so the gradient is a matrix.
 Returns
A map of variable to SciPy CSC sparse matrix; None if a variable value is missing.
 Return type
dict

is_dcp
(dpp: bool = False) → bool[source]¶ Checks whether the Expression is DCP.
 Parameters
dpp (
bool
, optional) – If True, enforce the disciplined parametrized programming (DPP) ruleset; only relevant when the problem involves Parameters. Returns
True if the Expression is DCP, False otherwise.
 Return type
bool

is_dgp
(dpp: bool = False) → bool[source]¶ Checks whether the Expression is loglog DCP.
 Returns
True if the Expression is loglog DCP, False otherwise.
 Return type
bool

abstract
is_dpp
(context='dcp') → bool[source]¶ The expression is a disciplined parameterized expression.

is_dqcp
() → bool[source]¶ Checks whether the Expression is DQCP.
 Returns
True if the Expression is DQCP, False otherwise.
 Return type
bool

property
ndim
¶ The number of dimensions in the expression’s shape.
 Type
int

abstract property
shape
¶ The expression dimensions.
 Type
tuple

property
sign
¶ The sign of the expression.
 Type
str

property
size
¶ The number of entries in the expression.
 Type
int

abstract property
value
¶ The numeric value of the expression.
 Type
NumPy.ndarray or None

property
Leaf¶

class
cvxpy.expressions.leaf.
Leaf
(shape: Tuple[int], value=None, nonneg: bool = False, nonpos: bool = False, complex: bool = False, imag: bool = False, symmetric: bool = False, diag: bool = False, PSD: bool = False, NSD: bool = False, hermitian: bool = False, boolean: bool = False, integer: bool = False, sparsity=None, pos: bool = False, neg: bool = False)[source]¶ Bases:
cvxpy.expressions.expression.Expression
A leaf node of an expression tree; i.e., a Variable, Constant, or Parameter.
A leaf may carry attributes that constrain the set values permissible for it. Leafs can have no more than one attribute, with the exception that a leaf may be both
nonpos
andnonneg
or bothboolean
in some indices andinteger
in others.An error is raised if a leaf is assigned a value that contradicts one or more of its attributes. See the
project
method for a convenient way to project a value onto a leaf’s domain. Parameters
shape (
tuple
orint
) – The leaf dimensions. Either an integer n for a 1D shape, or a tuple where the semantics are the same as NumPy ndarray shapes. Shapes cannot be more than 2D.value (
numeric type
) – A value to assign to the leaf.nonneg (
bool
) – Is the variable constrained to be nonnegative?nonpos (
bool
) – Is the variable constrained to be nonpositive?complex (
bool
) – Is the variable complex valued?symmetric (
bool
) – Is the variable symmetric?diag (
bool
) – Is the variable diagonal?PSD (
bool
) – Is the variable constrained to be positive semidefinite?NSD (
bool
) – Is the variable constrained to be negative semidefinite?Hermitian (
bool
) – Is the variable Hermitian?boolean (
bool
orlist
oftuple
) – Is the variable boolean? True, which constrains the entire Variable to be boolean, False, or a list of indices which should be constrained as boolean, where each index is a tuple of length exactly equal to the length of shape.integer (
bool
orlist
oftuple
) – Is the variable integer? The semantics are the same as the boolean argument.sparsity (
list
oftuplewith
) – Fixed sparsity pattern for the variable.pos (
bool
) – Is the variable positive?neg (
bool
) – Is the variable negative?

property
T
¶ The transpose of the expression.
 Type

property
ndim
¶ The number of dimensions in the expression’s shape.
 Type
int

project
(val)[source]¶ Project value onto the attribute set of the leaf.
A sensible idiom is
leaf.value = leaf.project(val)
. Parameters
val (
numeric type
) – The value assigned. Returns
The value rounded to the attribute type.
 Return type
numeric type

property
shape
¶ The dimensions of the expression.
 Type
tuple

property
size
¶ The number of entries in the expression.
 Type
int

property
value
¶ The numeric value of the parameter.
 Type
NumPy.ndarray or None
Variable¶

class
cvxpy.expressions.variable.
Variable
(shape=(), name=None, var_id=None, **kwargs)[source]¶ Bases:
cvxpy.expressions.leaf.Leaf
The optimization variables in a problem.

property
T
¶ The transpose of the expression.
 Type

property
ndim
¶ The number of dimensions in the expression’s shape.
 Type
int

project
(val)¶ Project value onto the attribute set of the leaf.
A sensible idiom is
leaf.value = leaf.project(val)
. Parameters
val (
numeric type
) – The value assigned. Returns
The value rounded to the attribute type.
 Return type
numeric type

project_and_assign
(val) → None¶ Project and assign a value to the variable.

property
shape
¶ The dimensions of the expression.
 Type
tuple

property
size
¶ The number of entries in the expression.
 Type
int

property
value
¶ The numeric value of the parameter.
 Type
NumPy.ndarray or None

property
Parameter¶

class
cvxpy.expressions.constants.parameter.
Parameter
(shape=(), name=None, value=None, id=None, **kwargs)[source]¶ Bases:
cvxpy.expressions.leaf.Leaf
Parameters in optimization problems.
Parameters are constant expressions whose value may be specified after problem creation. The only way to modify a problem after its creation is through parameters. For example, you might choose to declare the hyperparameters of a machine learning model to be Parameter objects; more generally, Parameters are useful for computing tradeoff curves.

property
T
¶ The transpose of the expression.
 Type

property
ndim
¶ The number of dimensions in the expression’s shape.
 Type
int

project
(val)¶ Project value onto the attribute set of the leaf.
A sensible idiom is
leaf.value = leaf.project(val)
. Parameters
val (
numeric type
) – The value assigned. Returns
The value rounded to the attribute type.
 Return type
numeric type

project_and_assign
(val) → None¶ Project and assign a value to the variable.

property
shape
¶ The dimensions of the expression.
 Type
tuple

property
size
¶ The number of entries in the expression.
 Type
int

property
value
¶ The numeric value of the parameter.
 Type
NumPy.ndarray or None

property
Constant¶

class
cvxpy.expressions.constants.
Constant
(value)[source]¶ Bases:
cvxpy.expressions.leaf.Leaf
A constant value.
Raw numerical constants (Python primite types, NumPy ndarrays, and NumPy matrices) are implicitly cast to constants via Expression operator overloading. For example, if
x
is an expression andc
is a raw constant, thenx + c
creates an expression by castingc
to a Constant.
property
T
¶ The transpose of the expression.
 Type

property
ndim
¶ The number of dimensions in the expression’s shape.
 Type
int

property
shape
¶ Returns the (row, col) dimensions of the expression.

property
size
¶ The number of entries in the expression.
 Type
int

property
value
¶ The numeric value of the constant.
 Type
NumPy.ndarray or None

property