References
- Casas E, Kruse F, Kunisch K. Optimal control of semilinear parabolic equations by BV-functions. SIAM J Control Optim. 2017;55:1752–1788.
- Engel S, Vexler B, Trautmann P. Optimal finite element error estimates for an optimal control problem governed by the wave equation with controls of bounded variation. IMA J Numer Anal. 2020;41(4): 2639–2667.
- Hafemeyer D, Mannel F, Neitzel I, et al. Finite element error estimates for one-dimensional elliptic optimal control by BV-functions. Math Control Relat Fields. 2020;10:333–363.
- Little MA, Jones NS. Generalized methods and solvers for noise removal from piecewise constant signals. I. background theory. Proc R Soc A Math Phys Eng Sci. 2011;467:3088–3114.
- Rudin LI, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms. Phys D Nonlin Phenom. 1992;60:259–268.
- Huang J, Zhang T. The benefit of group sparsity. Ann Stat. 2010;38:1978–2004.
- Barbero l., Sra S. Fast newton-type methods for total variation regularization. In: Proceedings of the 28th international conference on machine learning. ICML; 2011. p. 313–320.
- Condat L. A direct algorithm for 1-D total variation denoising. IEEE Signal Process Lett. 2013;20:1054–1057.
- Karahanoglu FI, Bayram L, Van De Ville D. A signal processing approach to generalized 1-D total variation. IEEE Trans Signal Process. 2011;59:5265–5274.
- Wahlberg B, Boyd S, Annergren M, et al. An ADMM algorithm for a class of total variation regularized estimation problems*. IFAC Proc Vol. 2012;45:83–88.
- Clason C, Kunisch K. A duality-based approach to elliptic control problems in non-reflexive Banach spaces. ESAIM Control Optim Calc Var. 2011;17:243–266.
- Hafemeyer D, Mannel F. A path-following inexact Newton method for optimal control in BV. 2020. https://arxiv.org/abs/2010.11628.
- Boyd N, Schiebinger G, Recht B. The alternating descent conditional gradient method for sparse inverse problems. SIAM J Optim. 2017;27:616–639.
- Bredies K, Pikkarainen HK. Inverse problems in spaces of measures. ESAIM Control Optim Calc Var. 2013;19:190–218.
- Denoyelle Q, Duval V, Peyré G, et al. The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy. Inverse Probl. 2020;36:42, Id/No 014001.
- Flinth A, de Gournay F, Weiss P. On the linear convergence rates of exchange and continuous methods for total variation minimization. Math Program. 2020;190:221–257.
- Pieper K, Walter D. Linear convergence of accelerated conditional gradient algorithms in spaces of measures. ESAIM Control Optim Calc Var. 2021;27:37, Id/No 38.
- Boyd N, Hastie T, Boyd S, et al. Saturating splines and feature selection. J Mach Learn Res. 2018;18:32, Id/No 197.
- Herrmann M, Herzog R, Kröner H, et al. Analysis and an interior-point approach for TV image reconstruction problems on smooth surfaces. SIAM J Imaging Sci. 2018;11:889–922.
- Hintermüller M, Kunisch K. Total bounded variation regularization as a bilaterally constrained optimization problem. SIAM J Appl Math. 2004;64:1311–1333.
- Grasmair M. The equivalence of the Taut string algorithm and BV-Regularization. J Math Imaging Vis. 2007;27:59–66.
- Hinterberger W, Hintermüller M, Kunisch K, et al. Tube methods for BV regularization. J Math Imaging Vis. 2003;19:219–235.
- Ambrosio L, Fusco N, Pallara D. Functions of bounded variation and free discontinuity problems. Oxford: Clarendon Press; 2000.
- Walter D. On sparse sensor placement for parameter identification problems with partial differential equations [dissertation]. München: Technische Universität München; 2019.
- Dunn JC. Convergence rates for conditional gradient sequences generated by implicit step length rules. SIAM J Control Optim. 1980;18:473–487.
- Milzarek A, Ulbrich M. A semismooth Newton method with multidimensional filter globalization for l1-Optimization. SIAM J Optim. 2014;24:298–333.
- Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci. 2009;2:183–202.
- Chambolle A, Dossal C. On the convergence of the iterates of the ‘Fast iterative shrinkage/thresholding algorithm’. J Optim Theory Appl. 2015;166:968–982.
- Kunisch K, Trautmann P, Vexler B. Optimal control of the undamped linear wave equation with measure valued controls. SIAM J Control Optim. 2016;54:1212–1244.
- Triggiani R. Regularity of wave and plate equations with interior point control. Atti Della Accademia Nazionale Dei Lincei. Classe Di Scienze Fisiche, Matematiche E Naturali. Rendiconti Lincei. Serie IX. Matematica E Applicazion. 1991;2:307–315.
- Duval V, Peyré G. Exact support recovery for sparse spikes deconvolution. Found Comput Math. 2015;15:1315–1355.