Aerial navigation in obstructed environments with embedded nonlinear model predictive control

Alpaqa: A matrix-free solver for nonlinear MPC and large-scale nonconvex optimization

“…PANOC is a quasi-Newton-accelerated first-order method, which -despite its simple, inexpensive iterations -enjoys locally superlinear convergence, without requiring the manipulation of large Jacobian or Hessian matrices. Applying ALM and penaltybased methods combined with PANOC has recently proven successful within several applications in NMPC [5], [6] and the Optimization Engine (OPEN) software [7], which shares some of its algorithmic foundations with the present work, although it is tailored more heavily towards embedded systems applications.…”

“…This phenomenon does not affect the global convergence of the algorithm. However, in the interest of practical performance, it is beneficial to reject these low-quality L-BFGS steps, as two problems arise when such steps are accepted: (1) it is likely that the next iterate will be (much) farther away from the optimum than before; and (2) the local curvature of ψ might be much larger at x k+1 , demanding a significant reduction of the step size γ in the next iteration in order to satisfy equation (6). The combined effect of ending up far away from the optimum and having to advance with small steps is detrimental for performance.…”