Online Active Set Strategy
- Start from a primal-dual feasible point
- Track active set (constraints at bounds)
- Update active set incrementally when parameters change Efficient for parametric QPs where data varies smoothly.
Mathematical Formulation
lb <= x <= ub (bounds)
Key methods:
- init(): First QP solve (cold start)
- hotstart(): Subsequent solves with modified data
Complexity
O(n^3) worst case per iteration, but typically much faster due to hot-starting and sparse updates.
Implementations
qpOASES
- QProblem.hpp - QP solver with general linear constraints
Solves convex QPs with bounds and linear constraints: