A review on sparse solutions in optimal control of partial differential equations

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Casas, E., Herzog, R., Wachsmuth, G.: Optimality conditions and error analysis of semilinear elliptic control problems with $${L}^1$$ L 1 cost functional. SIAM J. Optim. 22(3), 795–820 (2012)

Casas, E., Herzog, R., Wachsmuth, G.: Analysis of spatio-temporally sparse optimal control problems of semilinear parabolic equations. ESAIM Control Optim. Calc. Var. 23, 263–295 (2017)

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Casas, E., Kunisch, K.: Parabolic control problems in space-time measure spaces. ESAIM Control Optim. Calc. Var. 22(2), 355–370 (2016)

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Casas, E., Tröltzsch, F.: Second-order and stability analysis for state-constrained elliptic optimal control problems with sparse controls. SIAM J. Control Optim. 52(2), 1010–1033 (2014)

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Wachsmuth, D., Wachsmuth, G.: Convergence and regularisation results for optimal control problems with sparsity functional. ESAIM Control Optim. Calc. Var. 17(3), 858–886 (2011)

Wachsmuth, D., Wachsmuth, G.: Regularization error estimates and discrepancy principle for optimal control problems with inequality constraints. Control Cybern. 40(4), 1125–1158 (2011)