## CVXPY in Python

Here’s a basic example of using $CVXPY$, a $Python$ library for **convex optimization**.

This example solves a simple **linear programming problem**:

## Problem

Minimize the function $( c^T x )$ subject to the constraint $( Ax \leq b )$ and $( x \geq 0 )$, where:

- $( c )$ is a vector of coefficients for the objective function.
- $( A )$ is a matrix of coefficients for the inequality constraints.
- $( b )$ is a vector representing the upper bounds for the constraints.

## Sample Code

1 | import cvxpy as cp |

## Explanation

**Objective Function:**`c @ x`

is the dot product of the vector`c`

with the variable vector`x`

. We aim to minimize this value.**Constraints:**`A @ x <= b`

represents the inequality constraints, and`x >= 0`

ensures that the variables are non-negative.**Optimization:**`problem.solve()`

solves the**optimization**problem, and the optimal solution is stored in`x.value`

.

## Output

When you run this code, it will output the status of the **optimization** (e.g., “optimal”), the optimal value of the objective function, and the optimal values of the decision variables $( x )$.

1 | Status: optimal |

This example is a basic introduction, but $CVXPY$ can handle more complex problems, including quadratic programming, mixed-integer programming, and other types of **convex optimization problems**.