Today, different solvers for MATLAB exist for convex sum-of-squares problems. Most of these toolboxes bring their own implementation of a polynomial type. They also come with individual interfaces for both constraints and solutions.
The SOSFactory toolbox aims to provide a unified interface for polynomials, constraints, and solvers. It does not provide a polynomial class or a sum-of-squares solver itself. Instead, the relevant third-party source files must be accessible to MATLAB throughout the application.
At its core, for each pair of SOS solver / polynomial implementation, three classes provide the common interface:
- Factory : The factory class, with its interface defined in
AbstractSOSFactory.m, constitutes the entry-point for each solver. It provides basic polynomial operations (such as constructors, computation of jacobian, and checks) and allows to generate individual constraint and option objects. - Constraints : The constraints class (
AbstractSOSConstraints.m) collects the SOS constraints to describe a SOS problem and generates decision variable. It supports non-negativity constraints for scalars, matrices (positive semi-definiteness), and polynomials (sum-of-squares). Calling the respective solver is facilitated through theoptimizemethod of the constraint object (specific constraint implementation may provide additional optimisation methods). - Solution : The solution class (
AbstractSOSSolution.m) is solely return by the optimisation method of the constraint object and provides information and results of a sum-of-squares optimisation. The resulting values of the decision variables are accessible through thesubsmethod.
To date, SOSFactory supports sosopt and SPOT; but any toolbox can be added provided the interface described above (and defined in the abstract super-classes) is implemented.
The sosopt constraint class supports quasi-convex optimisation.
The SPOT factory / constraint classes support DSOS constraints through different implementations of AbstractSOSConstrains.