Multigrid optimization methods for linear and bilinear elliptic optimal control problems
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Multigrid optimization schemes that solve elliptic linear and bilinear optimal control problems are discussed. For the solution of these problems, the multigrid for optimization (MGOPT) method and the collective smoothing multigrid (CSMG) method are developed and compared. It is shown that though these two methods are formally similar, they provide different approaches to computational optimization with partial differential equations.
AMS Subject Classifications49K20 65N06 65N55
Keywordselliptic optimal control problems multigrid methods
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- 9.Lewis, R. M., Nash, S. G.: A multigrid approach to the optimization of systems governed by differential equations. AIAA-2000-4890, 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, CA (2000)Google Scholar