Augmented Lagrangian

[aj463]

A flexible augmented Lagrangian (AL) capability.

• PolyhedralProjection now derives from a new Projection base class.

• Problem has a new addConstraint overload through which users can pass a Constraint and Projection to implement $T(x)\in C.$ See the ALESQP paper. The Constraint corresponds to $T(x)$, and the Projection corresponds to projection on $C$ (a convex set).

• Problem enforces unique constraint names. Users can "group" together collections of constraints for penalization through a new addConstraintGroup member of Problem.

• The AL framework processes "ungrouped" constraints as follows. (1) Penalize inequalities. (2) Add linear equalities to the subproblem. (3) If present, add nonlinear equalities to the subproblem and penalize bounds. Else, (4) if present, add bounds to the subproblem.

It would help to discuss the following.

• Output of the AL algorithm. What is the best way to obtain stationarity measures for the different subproblems?

• Default scalings for penalized constraints.

[dridzal]

At a high level, this looks good.