Multigrid One Shot Methods for Optimal Control Problems

Download or read book Multigrid One Shot Methods for Optimal Control Problems written by National Aeronautics and Space Adm Nasa and published by . This book was released on 2018-10-22 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. ln this case, the control variable is a function whose discrete representation involves_an increasing number of variables with grid refinement. The minimization algorithm uses Lagrange multipliers to calculate sensitivity gradients. A preconditioned gradient descent algorithm is accelerated by a set of coarse grids. It optimizes for different scales in the representation of the control variable on different discretization levels. An analysis which reduces the problem to the boundary is introduced. It is used to approximate the two level asymptotic convergence rate, to determine the amplitude of the minimization steps, and the choice of a high pass filter to be used when necessary. The effectiveness of the method is demonstrated on a series of test problems. The new method enables the solutions of optimal control problems at the same cost of solving the corresponding analysis problems just a few times. Arian, Eyal and Taasan, Shlomo Unspecified Center NAS1-19480; RTOP 505-90-52-01...