Tutorials

CDOpt is an easy-to-use modular package that separates the manifold modules, the problem descriptions, the automatic differentiation packages, and solvers apart. All of the automatic differentiations are done behind the scenes so the amount of setup that the user needs to do is minimal. Usually, only the following steps are required:

1. Instantiate a manifold \(\mathcal{M}\) from the cdopt.manifold or define \(\mathcal{M} = \{x \in \mathbb{R}^n: c(x) = 0 \}\) by the cdopt.core.basic_manifold module.

2. Define a cost function \(f\) to minimize over the manifold \(\mathcal{M}\).

3. Using the cdopt.core.problem as a high-level interface to describe the optimization problem.

4. Retrieve the corresponding constraint dissolving function and its differentials from the problem object. Instantiate a solver from various of existing packages, including scipy.optimize and torch.optim, to minimize the constraint dissolving function without any constraints.

It is worth mentioning that the problem class in CDOpt integrates various pre-processing and concurrency checking steps for the optimization problems. Moreover, it provides integrated APIs for calling the related solvers. Therefore, although we can run the solvers without the cdopt.core.problem interface, using cdopt.core.problem to define the problem is always recommended.

• Quickstart
• Training neural networks with manifold constraints
• Define your own manifold