14,424 research outputs found
Fast iterative solvers for convection-diffusion control problems
In this manuscript, we describe effective solvers for the optimal control of stabilized convection-diffusion problems. We employ the local projection stabilization, which we show to give the same matrix system whether the discretize-then-optimize or optimize-then-discretize approach for this problem is used. We then derive two effective preconditioners for this problem, the �first to be used with MINRES and the second to be used with the Bramble-Pasciak Conjugate Gradient method. The key components of both preconditioners are an accurate mass matrix approximation, a good approximation of the Schur complement, and an appropriate multigrid process to enact this latter approximation. We present numerical results to demonstrate that these preconditioners result in convergence in a small number of iterations, which is robust with respect to the mesh size h, and the regularization parameter β, for a range of problems
Online algorithms for POMDPs with continuous state, action, and observation spaces
Online solvers for partially observable Markov decision processes have been
applied to problems with large discrete state spaces, but continuous state,
action, and observation spaces remain a challenge. This paper begins by
investigating double progressive widening (DPW) as a solution to this
challenge. However, we prove that this modification alone is not sufficient
because the belief representations in the search tree collapse to a single
particle causing the algorithm to converge to a policy that is suboptimal
regardless of the computation time. This paper proposes and evaluates two new
algorithms, POMCPOW and PFT-DPW, that overcome this deficiency by using
weighted particle filtering. Simulation results show that these modifications
allow the algorithms to be successful where previous approaches fail.Comment: Added Multilane sectio
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