⏱️ Help us benchmark CVXPY solvers! Contribute problems and results to the Solver Benchmarks project. 📅 The CVXPY developers are hosting listening sessions to learn more about what you are using CVXPY for and how we can better serve you. These examples show many different ways to use CVXPY.

What is CVXPY? Changing the problem · Infeasible and unbounded problems · Other problem statuses · Vectors and matrices · Constraints · Parameters · Custom Labels · Next steps · Atomic Functions · Operators · Scalar functions · Functions along an axis · Elementwise functions · Vector/matrix functions · Disciplined Convex Programming · Expressions · Sign · Curvature · Curvature rules · Infix operators · Example 1 ·

CVXPY is an open source Python-embedded modeling language for convex optimization problems. It lets you express your problem in a natural way that follows the math, rather than in the restrictive standard form required by solvers. For example, the following code solves a least-squares problem with box constraints:

CVXPY now supports N-dimensional expressions. This allows one to define variables, parameters, and constants with arbitrary number of dimensions. This new feature enables users to model problems with multi-dimensional data in a more natural way. In the example below, we consider a problem where the goal is to optimize the usage of a resource across multiple locations, days, and hours.

import cvxpy as cp import numpy as np # Create variables weights = cp.Variable(3, name="weights") # Create constraints with custom labels constraints = [ (weights >= 0).set_label("non_negative_weights"), (cp.sum(weights) == 1).set_label("budget_constraint"), (weights <= 0.4).set_label("concentration_limits") ] # Create expressions with custom labels (portfolio example) # Expected returns and covariance (toy data for illustration) mu = np.array([0.08, 0.10, 0.07]) Sigma = np.array([[0.10, 0.02, 0.01], [0.02, 0.08, 0.03], [0.01, 0.03, 0.09]]) expected_return = (mu @ weights).set_label("expected_

⏱️ Help us benchmark CVXPY solvers! Contribute problems and results to the Solver Benchmarks project. 📅 The CVXPY developers are hosting listening sessions to learn more about what you are using CVXPY for and how we can better serve you. These examples show many different ways to use CVXPY.

June 18, 2023 - What is CVXPY library? How to do covex optimization using CVXPY in Python? Simple example of convex optimization using CVXPY.

CVXPY is a Python-embedded modeling language for convex optimization problems. It allows you to express your problem in a natural way that follows the math, rather than in the restrictive standard form required by solvers. For example, the following code solves a least-squares problem where the variable is constrained by lower and upper bounds:

For example, we might have \(n\) different products, each constructed out of \(m\) components. Each entry \(A_{ij}\) is the amount of component \(i\) required to build one unit of product \(j\). Each entry \(b_i\) is the total amount of component \(i\) available.

What is CVXPY? Changing the problem · Infeasible and unbounded problems · Other problem statuses · Vectors and matrices · Constraints · Parameters · Atomic Functions · Operators · Scalar functions · Functions along an axis · Elementwise functions · Vector/matrix functions · Disciplined Convex Programming · Expressions · Sign · Curvature · Curvature rules · Infix operators · Example 1 ·

Indexing drops dimensions while slicing preserves dimensions. For example, x = cvxpy.Variable(5) print("0 dimensional", x[0].shape) print("1 dimensional", x[0:1].shape)

The infix operators +, -, *, / and matrix multiplication @ are treated exactly like functions. The infix operators + and - are affine, so the rules above are used to flag the curvature. For example, expr1 + expr2 is flagged as convex if expr1 and expr2 are convex.

A simple example of a quadratic program arises in finance. Suppose we have \(n\) different stocks, an estimate \(r \in \mathcal{R}^n\) of the expected return on each stock, and an estimate \(\Sigma \in \mathcal{S}^{n}_+\) of the covariance of the returns.

# np.log(trAtA) ]) # Add row to matrix A A = spa.vstack((A, spa.csc_matrix(A_temp)), 'csc') # Add bounds on v l = np.log(problem['rho_min'].iloc[0]) u = np.log(problem['rho_max'].iloc[0]) v_l = np.append(v_l, l) v_u = np.append(v_u, u) # # Define CVXPY problem alpha = cvxpy.Variable(n_params) v = cvxpy.Variable(n_problems) constraints = [v_l &lt;= v, v &lt;= v_u] cost = cvxpy.norm(A * alpha - v) objective = cvxpy.Minimize(cost) problem = cvxpy.Problem(objective, constraints) # Solve problem print("Solving problem with CVXPY and GUROBI") problem.solve(solver=cvxpy.MOSEK, verbose=True) print("Solution status: %s" % problem.status) # Get learned alpha alpha_fit = np.asarray(alpha.value).flatten()

The Basic examples section shows how to solve some common optimization problems in CVXPY.

To see the object-oriented approach applied to more complex flow problems, look in the cvxpy/examples/flows/ directory.

ckages (from cvxpy) (1.11.2)\n", "Requirement already satisfied: setuptools>65.5.1 in /usr/local/lib/python3.10/dist-packages (from cvxpy) (67.7.2)\n", "Requirement already satisfied: qdldl in /usr/local/lib/python3.10/dist-packages (from osqp>=0.4.1->cvxpy) (0.1.7.post0)\n" ] } ] }, { "cell_type": "markdown", "source": [ "You will generally just need to run pip install for cvxpy.

These examples show many different ways to use CVXPY. The Basic Examples section shows how to solve some common optimization problems in CVXPY.

A Python-embedded modeling language for convex optimization problems. - cvxpy/examples/notebooks/WWW/sparse_solution.ipynb at master · cvxpy/cvxpy

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