Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional
نویسندگان
چکیده
منابع مشابه
Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional
First-order proximal methods that solve linear and bilinear elliptic optimal control problems with a sparsity cost functional are discussed. In particular, fast convergence of these methods is proved. For benchmarking purposes, inexact proximal schemes are compared to an inexact semismooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectivene...
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Theorem 4.3 Let the initialization u0 be sufficiently close to the solution ū of P. Then the iterates uk of Algorithm 1 converge superlinearly to ū in L2(Ω). Moreover, the corresponding states yk converge superlinearly to ȳ in H1 0 (Ω). Proof To apply Theorem 4.1, it remains to show that the generalized derivative (4.7) is invertible and that the norms of the inverse linear mappings are bounded...
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ژورنال
عنوان ژورنال: Applied Mathematics
سال: 2016
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2016.79086