> ## Documentation Index
> Fetch the complete documentation index at: https://prod-mint.classiq.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Combinatorial Optimization

The Classiq combinatorial optimization platform is a quantum software engine for optimization problems that you define.
The engine tackles your formulated real-world optimization challenges and generates customized quantum programs.
You choose whether to run the programs on a quantum backend or a classical simulation, and receive the optimized solution.
To gain further insights regarding the synthesis process, you can examine the synthesized program with the
Classiq [analyzer](/user-guide/analysis/index) module.

## Formulating Problems

You describe new optimization problems using the Python SDK package.
The problem is formulated using [PYOMO](http://www.pyomo.org/), a Python-based, open-source optimization
modeling language. The language supports a wide variety of problem types, such as integer linear
programming, quadratic programming, graph theory problems, and SAT problems.
Read in-depth reviews of the language’s capabilities in
\[ \[1] ]\(#pyomo documentation) and \[ \[2] ]\(#pyomo cookbook) \[ \[3] ]\(#pyomo intro).
The basics of problem modelling in PYOMO and
a complete example are in the [problem formulation](/user-guide/applications/optimization/problem-formulation) section.

The platform supports an extensive set of modeling configurations for your use ([supported modeling](/user-guide/applications/optimization/supported-modeling)).

## Solving Optimization Problems

The core Classiq capabilities are generation of a designated quantum solution,
and execution of the generated algorithm on a quantum backend.

The platform relies on the QAOA penalty algorithm to solve optimization problems.

## References

<a name="pyomo documentation">\[1]</a> Pyomo Documentation 6.0.1, [https://pyomo.readthedocs.io/en/stable/](https://pyomo.readthedocs.io/en/stable/).

<a name="pyomo cookbook">\[2]</a> Prof. Jeffrey Kantor’s Pyomo Cookbook
[https://jckantor.github.io/ND-Pyomo-Cookbook/](https://jckantor.github.io/ND-Pyomo-Cookbook/).

<a name="pyomo intro">\[3]</a> J. D. Siirola, Introduction to Pyomo: The optimization foundation for IDAES,
[https://www.osti.gov/servlets/purl/1524963](https://www.osti.gov/servlets/purl/1524963) (2018).