Summary
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.
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Vallejos, M., Borzì, A. Multigrid optimization methods for linear and bilinear elliptic optimal control problems. Computing 82, 31–52 (2008). https://doi.org/10.1007/s00607-008-0261-7
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DOI: https://doi.org/10.1007/s00607-008-0261-7