Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 37
Number of page(s) 40
DOI https://doi.org/10.1051/cocv/2026011
Published online 24 April 2026
  1. K. Bredies and H.K. Pikkarainen, Inverse problems in spaces of measures. ESAIM: Control Optim. Calc. Var. 19 (2013) 190–218. [Google Scholar]
  2. O. Scherzer and B. Walch, Sparsity regularization for radon measures, in Scale Space and Variational Methods in Computer Vision, edited by X.-C. Tai, K. Mørken, M. Lysaker and K.-A. Lie, editors. Springer Berlin Heidelberg, Berlin, Heidelberg (2009) 452–463. [Google Scholar]
  3. K. Kunisch, P. Trautmann and B. Vexler, Optimal control of the undamped linear wave equation with measure valued controls. SIAM J. Control Optim. 54 (2016) 1212–1244. [CrossRef] [MathSciNet] [Google Scholar]
  4. K. Pieper, B.Q. Tang, P. Trautmann and D. Walter, Inverse point source location with the Helmholtz equation on a bounded domain. Computat. Optim. Appl. 77 (2020) 213–249. [Google Scholar]
  5. Q. Denoyelle, V. Duval, G. Peyre and E. Soubies, The sliding Frank-Wolfe algorithm and its application to super-resolution microscopy. Inverse Probi. 36 (2020) 014001. [Google Scholar]
  6. C.W. McCutchen, Superresolution in microscopy and the abbe resolution limit. J. Opt. Soc. Am. 57 (1967) 1190–1192. [Google Scholar]
  7. E. Casas, C. Clason and K. Kunisch, Approximation of elliptic control problems in measure spaces with sparse solutions. SIAM J. Control Optim. 50 (2012) 1735–1752. [Google Scholar]
  8. C. Clason and K. Kunisch, A measure space approach to optimal source placement. Comput. Optim. Appl. 53 (2012) 155–171. [Google Scholar]
  9. K. Pieper and B. Vexler, A priori error analysis for discretization of sparse elliptic optimal control problems in measure space. SIAM J. Control Optim. 51 (2013) 2788–2808. [Google Scholar]
  10. F. Bach. Breaking the curse of dimensionality with convex neural networks. J. Mach. Learn. Res. 18 (2017) 53. [Google Scholar]
  11. J. Kiefer and J. Wolfowitz, Optimum designs in regression problems. Ann. Math. Stat. 30 (1959) 271–294. [Google Scholar]
  12. I. Neitzel, K. Pieper, B. Vexler and D. Walter, A sparse control approach to optimal sensor placement in PDE- constrained parameter estimation problems. Numer. Math. 143 (2019) 943–984. [Google Scholar]
  13. C. Boyer, A. Chambolle, Y. De Castro, V. Duval, F. de Gournay and P. Weiss, On representer theorems and convex regularization. SIAM J. Optim. 29 (2019) 1260–1281. [Google Scholar]
  14. K. Bredies and M. Carioni, Sparsity of solutions for variational inverse problems with finite-dimensional data. Calc. Var. Part. Differ. Equ. 59 (2020) Paper No. 14. [Google Scholar]
  15. K. Pieper and D. Walter, Linear convergence of accelerated conditional gradient algorithms in spaces of measures. ESAIM Control Optim. Calc. Var. 27 (2021) Paper No. 38, 37. [Google Scholar]
  16. V. Duval and G. Peyre, Exact support recovery for sparse spikes deconvolution. Found. Computat. Math. 15 (2014) 1315–1355. [Google Scholar]
  17. L. Chizat, Sparse optimization on measures with over-parameterized gradient descent. Math. Program. 194 (2022) 487–532. [Google Scholar]
  18. A. Flinth, F. de Gournay and P. Weiss, On the linear convergence rates of exchange and continuous methods for total variation minimization. Math. Program. 190 (2021) 221–257. [Google Scholar]
  19. C. Christof and G. Wachsmuth, Differential sensitivity analysis of variational inequalities with locally Lipschitz continuous solution operators. Appl. Math. Optim. 81 (2020) 23–62. [Google Scholar]
  20. R.T. Rockafellar and R.J.B. Wets, Variational Analysis. Springer Berlin Heidelberg (1998). [Google Scholar]
  21. M. Benko and P. Mehlitz, Why second-order sufficient conditions are, in a way, easy - or - revisiting calculus for second subderivatives. J. Convex Anal. 30 (2023) 541–589. [Google Scholar]
  22. C.N. Do, Generalized second-order derivatives of convex functions in reflexive Banach spaces. Trans. Am. Math. Soc. 334 (1992) 281–301. [Google Scholar]
  23. C. Christof and G. Wachsmuth, No-gap second-order conditions via a directional curvature functional. SIAM J. Optim. 28 (2018) 2097–2130. [CrossRef] [MathSciNet] [Google Scholar]
  24. N. Borchard and G. Wachsmuth, Second-order conditions for spatio-temporally sparse optimal control via second subderivatives 5 (2024) 1–36. [Google Scholar]
  25. D. Wachsmuth and G. Wachsmuth, Second-order conditions for non-uniformly convex integrands: quadratic growth in L1. J. Nonsmooth Anal. Optim. 3 (2022) 1–36. [Google Scholar]
  26. P.-T. Huynh, K. Pieper and D. Walter, Towards optimal sensor placement for inverse problems in spaces of measures. Inverse Probl. 40 (2024) 1–43. [Google Scholar]
  27. C. Poon, N. Keriven and G. Peyre, Support localization and the fisher metric for off-the-grid sparse Regularization, in Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, vol. 89 of Proceedings of Machine Learning Research, edited by K. Chaudhuri and M. Sugiyama. PMLR (2019), 1341–1350. [Google Scholar]
  28. C. Poon, N. Keriven and G. Peyré, The geometry of off-the-grid compressed sensing. Found. Comput. Math. 23 (2023) 241–327. [Google Scholar]
  29. D. Leykekhman, B. Vexler and D. Walter, Numerical analysis of sparse initial data identification for parabolic problems. ESAIM Math. Model. Numer. Anal. 54 (2020) 1139–1180. [Google Scholar]
  30. P. Merino, I. Neitzel and F. Troltzsch, On linear-quadratic elliptic control problems of semi-infinite type. Appl. Anal. 90 (2011) 1047–1074. [Google Scholar]
  31. H.W. Alt, Lineare Funktionalanalysis, 6th edn. Springer, Berlin (2011). [Google Scholar]
  32. J. Borwein and Q. Zhu, Techniques of Variational Analysis. Springer-Verlag (2005). [Google Scholar]
  33. P. Hajlasz, P. Koskela and H. Tuominen, Sobolev embeddings, extensions and measure density condition. J. Funct. Anal. 254 (2008) 1217–1234. [Google Scholar]
  34. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer New York (2011). [Google Scholar]
  35. B. Piccoli, F. Rossi and M. Tournus, A Wasserstein norm for signed measures, with application to non-local transport equation with source term. Commun. Math. Sci. 21 (2023) 1279–1301. [Google Scholar]
  36. J. Frederic Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer, Berlin (2000). [Google Scholar]
  37. H.H. Bauschke and P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, Berlin (2011). [Google Scholar]

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