Multigrid One Shot Methods for Optimal Control Problems: Infinite Dimensional Control
Abstract
The multigrid one shot method for optimal control problems, governed by elliptic systems, is introduced for the infinite dimensional control space. In this case the control variable is a function whose discrete representation involves 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 step, 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. Optimal control, Optimal shape design, Multigrid, One-shot, Adjoint.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1994
- Accession Number
- ADA284376
Entities
People
- Eyal Arian
- Shlomo Ta'asan