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.

T
¶ Expression – The transpose of the expression.

__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: Expression

curvature
¶ str – The curvature of the expression.

domain
¶ list – The constraints describing the closure of the region where the expression is finite.

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
()[source]¶ Checks whether the constraint is DCP.
Returns: True if the constraint is DCP, False otherwise. Return type: bool

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

shape
¶ tuple – The expression dimensions.

sign
¶ str – The sign of the expression.

size
¶ int – The number of entries in the expression.

value
¶ NumPy.ndarray or None – The numeric value of the expression.

Leaf¶

class
cvxpy.expressions.leaf.
Leaf
(shape, value=None, nonneg=False, nonpos=False, complex=False, imag=False, symmetric=False, diag=False, PSD=False, NSD=False, hermitian=False, boolean=False, integer=False, sparsity=None)[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 or int) – 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 or list of tuple) – 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 or list of tuple) – Is the variable integer? The semantics are the same as the boolean argument.
 sparsity (list of tuplewith) – Fixed sparsity pattern for the variable.

T
¶ Expression – The transpose of the expression.

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

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

shape
¶ tuple – The dimensions of the expression.

size
¶ int – The number of entries in the expression.

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

T
¶ Expression – The transpose of the expression.

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

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)¶ Project and assign a value to the variable.

shape
¶ tuple – The dimensions of the expression.

size
¶ int – The number of entries in the expression.

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

Parameter¶

class
cvxpy.expressions.constants.parameter.
Parameter
(shape=(), name=None, value=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.

T
¶ Expression – The transpose of the expression.

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

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)¶ Project and assign a value to the variable.

shape
¶ tuple – The dimensions of the expression.

size
¶ int – The number of entries in the expression.

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

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.
T
¶ Expression – The transpose of the expression.

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

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

size
¶ int – The number of entries in the expression.

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