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---
title: LinearExpression (v0.29)
description: API reference for qiskit.optimization.problems.LinearExpression in qiskit v0.29
in_page_toc_min_heading_level: 1
python_api_type: class
python_api_name: qiskit.optimization.problems.LinearExpression
---
# LinearExpression
<Class id="qiskit.optimization.problems.LinearExpression" isDedicatedPage={true} github="https://github.com/qiskit-community/qiskit-aqua/tree/stable/0.9/qiskit/optimization/problems/linear_expression.py" signature="LinearExpression(quadratic_program, coefficients)" modifiers="class">
Bases: `qiskit.optimization.problems.quadratic_program_element.QuadraticProgramElement`
Representation of a linear expression by its coefficients.
Creates a new linear expression.
The linear expression can be defined via an array, a list, a sparse matrix, or a dictionary that uses variable names or indices as keys and stores the values internally as a dok\_matrix.
**Parameters**
* **quadratic\_program** (`Any`) The parent QuadraticProgram.
* **coefficients** (`Union`\[`ndarray`, `spmatrix`, `List`\[`float`], `Dict`\[`Union`\[`int`, `str`], `float`]]) The (sparse) representation of the coefficients.
## Methods
<span id="qiskit-optimization-problems-linearexpression-evaluate" />
### evaluate
<Function id="qiskit.optimization.problems.LinearExpression.evaluate" signature="LinearExpression.evaluate(x)">
Evaluate the linear expression for given variables.
**Parameters**
**x** (`Union`\[`ndarray`, `List`, `Dict`\[`Union`\[`int`, `str`], `float`]]) The values of the variables to be evaluated.
**Return type**
`float`
**Returns**
The value of the linear expression given the variable values.
</Function>
<span id="qiskit-optimization-problems-linearexpression-evaluate-gradient" />
### evaluate\_gradient
<Function id="qiskit.optimization.problems.LinearExpression.evaluate_gradient" signature="LinearExpression.evaluate_gradient(x)">
Evaluate the gradient of the linear expression for given variables.
**Parameters**
**x** (`Union`\[`ndarray`, `List`, `Dict`\[`Union`\[`int`, `str`], `float`]]) The values of the variables to be evaluated.
**Return type**
`ndarray`
**Returns**
The value of the gradient of the linear expression given the variable values.
</Function>
<span id="qiskit-optimization-problems-linearexpression-to-array" />
### to\_array
<Function id="qiskit.optimization.problems.LinearExpression.to_array" signature="LinearExpression.to_array()">
Returns the coefficients of the linear expression as array.
**Return type**
`ndarray`
**Returns**
An array with the coefficients corresponding to the linear expression.
</Function>
<span id="qiskit-optimization-problems-linearexpression-to-dict" />
### to\_dict
<Function id="qiskit.optimization.problems.LinearExpression.to_dict" signature="LinearExpression.to_dict(use_name=False)">
Returns the coefficients of the linear expression as dictionary, either using variable names or indices as keys.
**Parameters**
**use\_name** (`bool`) Determines whether to use index or names to refer to variables.
**Return type**
`Dict`\[`Union`\[`int`, `str`], `float`]
**Returns**
An dictionary with the coefficients corresponding to the linear expression.
</Function>
## Attributes
### coefficients
<Attribute id="qiskit.optimization.problems.LinearExpression.coefficients">
Returns the coefficients of the linear expression.
**Return type**
`dok_matrix`
**Returns**
The coefficients of the linear expression.
</Attribute>
### quadratic\_program
<Attribute id="qiskit.optimization.problems.LinearExpression.quadratic_program">
Returns the parent QuadraticProgram.
**Return type**
`Any`
**Returns**
The parent QuadraticProgram.
</Attribute>
</Class>