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---
title: QuadraticObjective
description: API reference for qiskit.optimization.problems.QuadraticObjective
in_page_toc_min_heading_level: 1
python_api_type: class
python_api_name: qiskit.optimization.problems.QuadraticObjective
---
<span id="qiskit-optimization-problems-quadraticobjective" />
# qiskit.optimization.problems.QuadraticObjective
<Class id="qiskit.optimization.problems.QuadraticObjective" isDedicatedPage={true} github="https://github.com/qiskit-community/qiskit-aqua/tree/stable/0.8/qiskit/optimization/problems/quadratic_objective.py" signature="QuadraticObjective(quadratic_program, constant=0.0, linear=None, quadratic=None, sense=<ObjSense.MINIMIZE: 1>)" modifiers="class">
Representation of quadratic objective function of the form: constant + linear \* x + x \* quadratic \* x.
Constructs a quadratic objective function.
**Parameters**
* **quadratic\_program** (`Any`) – The parent quadratic program.
* **constant** (`float`) – The constant offset of the objective.
* **linear** (`Union`\[`ndarray`, `spmatrix`, `List`\[`float`], `Dict`\[`Union`\[`int`, `str`], `float`], `None`]) – The coefficients of the linear part of the objective.
* **quadratic** (`Union`\[`ndarray`, `spmatrix`, `List`\[`List`\[`float`]], `Dict`\[`Tuple`\[`Union`\[`int`, `str`], `Union`\[`int`, `str`]], `float`], `None`]) – The coefficients of the quadratic part of the objective.
* **sense** (`ObjSense`) – The optimization sense of the objective.
### \_\_init\_\_
<Function id="qiskit.optimization.problems.QuadraticObjective.__init__" signature="__init__(quadratic_program, constant=0.0, linear=None, quadratic=None, sense=<ObjSense.MINIMIZE: 1>)">
Constructs a quadratic objective function.
**Parameters**
* **quadratic\_program** (`Any`) – The parent quadratic program.
* **constant** (`float`) – The constant offset of the objective.
* **linear** (`Union`\[`ndarray`, `spmatrix`, `List`\[`float`], `Dict`\[`Union`\[`int`, `str`], `float`], `None`]) – The coefficients of the linear part of the objective.
* **quadratic** (`Union`\[`ndarray`, `spmatrix`, `List`\[`List`\[`float`]], `Dict`\[`Tuple`\[`Union`\[`int`, `str`], `Union`\[`int`, `str`]], `float`], `None`]) – The coefficients of the quadratic part of the objective.
* **sense** (`ObjSense`) – The optimization sense of the objective.
</Function>
## Methods
| | |
| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------- |
| [`__init__`](#qiskit.optimization.problems.QuadraticObjective.__init__ "qiskit.optimization.problems.QuadraticObjective.__init__")(quadratic\_program\[, constant, …]) | Constructs a quadratic objective function. |
| [`evaluate`](#qiskit.optimization.problems.QuadraticObjective.evaluate "qiskit.optimization.problems.QuadraticObjective.evaluate")(x) | Evaluate the quadratic objective for given variable values. |
| [`evaluate_gradient`](#qiskit.optimization.problems.QuadraticObjective.evaluate_gradient "qiskit.optimization.problems.QuadraticObjective.evaluate_gradient")(x) | Evaluate the gradient of the quadratic objective for given variable values. |
## Attributes
| | |
| ------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------- |
| [`constant`](#qiskit.optimization.problems.QuadraticObjective.constant "qiskit.optimization.problems.QuadraticObjective.constant") | Returns the constant part of the objective function. |
| [`linear`](#qiskit.optimization.problems.QuadraticObjective.linear "qiskit.optimization.problems.QuadraticObjective.linear") | Returns the linear part of the objective function. |
| [`quadratic`](#qiskit.optimization.problems.QuadraticObjective.quadratic "qiskit.optimization.problems.QuadraticObjective.quadratic") | Returns the quadratic part of the objective function. |
| [`quadratic_program`](#qiskit.optimization.problems.QuadraticObjective.quadratic_program "qiskit.optimization.problems.QuadraticObjective.quadratic_program") | Returns the parent QuadraticProgram. |
| [`sense`](#qiskit.optimization.problems.QuadraticObjective.sense "qiskit.optimization.problems.QuadraticObjective.sense") | Returns the sense of the objective function. |
### Sense
<Attribute id="qiskit.optimization.problems.QuadraticObjective.Sense">
alias of `ObjSense`
</Attribute>
### constant
<Attribute id="qiskit.optimization.problems.QuadraticObjective.constant">
Returns the constant part of the objective function.
**Return type**
`float`
**Returns**
The constant part of the objective function.
</Attribute>
### evaluate
<Function id="qiskit.optimization.problems.QuadraticObjective.evaluate" signature="evaluate(x)">
Evaluate the quadratic objective for given variable values.
**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 quadratic objective given the variable values.
</Function>
### evaluate\_gradient
<Function id="qiskit.optimization.problems.QuadraticObjective.evaluate_gradient" signature="evaluate_gradient(x)">
Evaluate the gradient of the quadratic objective for given variable values.
**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 quadratic objective given the variable values.
</Function>
### linear
<Attribute id="qiskit.optimization.problems.QuadraticObjective.linear">
Returns the linear part of the objective function.
**Return type**
`LinearExpression`
**Returns**
The linear part of the objective function.
</Attribute>
### quadratic
<Attribute id="qiskit.optimization.problems.QuadraticObjective.quadratic">
Returns the quadratic part of the objective function.
**Return type**
`QuadraticExpression`
**Returns**
The quadratic part of the objective function.
</Attribute>
### quadratic\_program
<Attribute id="qiskit.optimization.problems.QuadraticObjective.quadratic_program">
Returns the parent QuadraticProgram.
**Return type**
`Any`
**Returns**
The parent QuadraticProgram.
</Attribute>
### sense
<Attribute id="qiskit.optimization.problems.QuadraticObjective.sense">
Returns the sense of the objective function.
**Return type**
`ObjSense`
**Returns**
The sense of the objective function.
</Attribute>
</Class>
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