Katana User Manual

A more in-depth guide on customising, tweaking and extending Katana.

Implementing Custom Separators

The Separator API is intended to abstract the logic of generating separating hyperplanes into two parts:

1. What stateful information is required? For example, the KatanaFirstOrderSeparator stores evaluated constraint values, evaluated constraint Jacobians, Jacobian sparsity structure, etc.

2. How is that information used to generate the cutting plane? In the default Newton-based algorithm, the hyperplane is constructed as a first-order expansion around a point.

Implementing a custom separator requires a distinction between the _information_ required and the _method_ used. It may not be necessary to create a new subclass of AbstractKatanaSeparator if, for example, the separation oracle only intends to use first-order information. Consider a method of generating cutting planes that involves starting at the LP optimal point $x^{*}$ and performing gradient descent until within some $\\epsilon$ of the constraint surface. Ideally, this would require another function that can be used as the algo of a KatanaFirstOrderSeparator.

On the other hand, if the custom separator requires second-order constraint values, such as the Hessian, it would be necessary to implement a new subclass of AbstractKatanaSeparator. It is then up to that implementation if the actual algorithm called by gencut is itself modular.

Visualising linear cuts

KatanaNonlinearModel provides a method to retrieve every linear cut generated during the solve process, as well as incremental LP solution vectors. Enable this feature by including :VisData in the list of features passed to KatanaSolver. Retrieve this information by calling getKatanaCuts and getKatanaSols respectively. See the library documentation for details.

An example approach to visualisation is provided here. Note that this script has external dependencies.

Expressing models in JuMP for better performance with Katana

TODO.