# Qiskit tutorials: Optimization¶

Click any link to open the tutorial directly in Quantum Lab.

Quadratic programs - In this tutorial, we briefly introduce how to build optimization problems using Qiskit’s optimization module. Qiskit introduces the

`QuadraticProgram`

class to make a model of a quadratically constrained optimization problem.Converters for quadratic programs Optimization algorithms are defined for a certain formulation of a quadratic program, and we need to convert our problem to the right type. To map a problem to the correct input format, the optimization module of Qiskit offers a variety of converters. This tutorial provides an overview of this functionality.

Minimum eigen optimizer - Qiskit provides automatic conversion from a suitable

`QuadraticProgram`

to an Ising Hamiltonian, which then allows you to leverage all the`MinimumEigenSolver`

methods. This lab illustrates the conversion from a`QuadraticProgram`

to an`Operator`

and then shows how to use the`MinimumEigenOptimizer`

with different`MinimumEigensolver`

to solve a given`QuadraticProgram`

.Grover optimizer - In this notebook we will explore each component of the

`GroverOptimizer`

, which utilizes the techniques described in Grover Adaptive Search (GAS) by minimizing a Quadratic Unconstrained Binary Optimization (QUBO) problem.ADMM optimizer - This tutorial illustrates how to use the ADMM optimizer. This optimizer can solve classes of mixed-binary constrained optimization problems, which often appear in logistic, finance, and operation research.

Max-cut and traveling salesman problem - This notebook discusses max-cut problems of practical interest in many fields, shows how they can be mapped on quantum computers manually, and illustrates how Qiskit’s optimization module supports this.

Vehicle routing - This tutorial describes how to solve a vehicle routing problem.

Improving variational quantum optimization using CVaR - This notebook shows how to use the Conditional Value at Risk (CVaR) objective function within the variational quantum optimization algorithms provided by Qiskit. Particularly, it demonstrates how to set up the

`MinimumEigenOptimizer`

using`VQE`

accordingly.