Augmented Lagrangian method for semidefinite constraints

[mohdibntarek]

One can generalize Percival's implementation to enable the use of slack models and the projected gradient method with semidefinite constraints. This will enable the use of the augmented Lagrangian algorithm on semidefinite constrained problems. One can even generalize the implementation to handle arbitrary convex cones supported in https://github.com/kul-forbes/ProximalOperators.jl.

[mohdibntarek]

The easiest way to implement this in a Julian way is to:

1. Make sure Percival can handle non-standard Julia array types gracefully.
2. Define an array type that is a mix of reals and SPD matrices.
3. Define arithmetic, gradient and projection functions on the fancy array type as well as any other function needed to make Percival work.