Open Access
Volume 30, 2024
Article Number 7
Number of page(s) 40
Published online 09 February 2024
  1. K. Bredies, M. Carioni, S. Fanzon and F. Romero, On the extremal points of the ball of the Benamou-†“Brenier energy. Bull. Land. Math. Soc. 53 (2021) 1436–1452. [Google Scholar]
  2. K. Bredies and S. Fanzon, An optimal transport approach for solving dynamic inverse problems in spaces of measures. ESAIM: M2AN 54 (2020) 2351–2382. [CrossRef] [EDP Sciences] [Google Scholar]
  3. G.S. Alberti, H. Ammari, F. Romero and T. Wintz, Dynamic spike superresolution and applications to ultrafast ultrasound imaging. SIAM J. Imaging Sci. 12 (2019) 1501–1527. [CrossRef] [MathSciNet] [Google Scholar]
  4. K. Bredies, M. Carioni and S. Fanzon, A superposition principle for the inhomogeneous continuity equation with Hellinger–Kantorovich-regular coefficients. arXiv preprint arXiv:2007.06964, 2020. [Google Scholar]
  5. K. Bredies, M. Carioni, S. Fanzon and F. Romero, A generalized conditional gradient method for dynamic inverse problems with optimal transport regularization. arXiv preprint arXiv:2012.11706, 2020. [Google Scholar]
  6. J.-M. Azaïs, Y. de Castro and F. Gamboa, Spike detection from inaccurate samplings. Appl. Computat. Harmonic Anal. 38 (2015) 177–195. [CrossRef] [Google Scholar]
  7. K. Bredies and H.K. Pikkarainen, Inverse problems in spaces of measures. ESAIM: Control Optim. Calc. Var. 19 (2013) 190–218. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  8. V. Duval and G. Peyré, Exact support recovery for sparse spikes deconvolution. Found. Computat. Math. 15 (2015) 1315–1355, 2015. [CrossRef] [Google Scholar]
  9. C. Poon, N. Keriven and G. Peyré, The geometry of off-the-grid compressed sensing. Found. Computat. Math. (2021). [Google Scholar]
  10. N. Boyd, G. Schiebinger and B. Recht, The alternating descent conditional gradient method for sparse inverse problems. SIAM J. Optim. 27 (2017) 616–639. [CrossRef] [MathSciNet] [Google Scholar]
  11. Q. Denoyelle, V. Duval, G. Peyre and E. Soubies, The Sliding Frank-Wolfe Algorithm and its application to super-resolution microscopy. Inverse Probl. (2019). [Google Scholar]
  12. M. Jaggi, Revisiting Frank–Wolfe: projection-free sparse convex Optimization, in International Conference on Machine Learning. PMLR (2013) 427–435. [Google Scholar]
  13. C. Boyer, A. Chambolle, Y.D. Castro, V. Duval, F. De Gournay and P. Weiss, On representer theorems and convex regularization. SIAM J. Optim. 29 (2019) 1260–1281. [CrossRef] [MathSciNet] [Google Scholar]
  14. K. Bredies and M. Carioni, Sparsity of solutions for variational inverse problems with finite-dimensional data. Calc. Var. Part. Diff. Eq. 59 (2019) 14. [Google Scholar]
  15. M. Unser, J. Fageot and J.P. Ward, Splines are Universal Solutions of linear inverse problems with generalized-tv regularization. SIAM Rev. 59 (2017) 769–793. [CrossRef] [MathSciNet] [Google Scholar]
  16. F. Santambrogio, Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling. Progress in Nonlinear Differential Equations and Their Applications. Springer International Publishing (2015). [Google Scholar]
  17. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows: In Metric Spaces and in the Space of Probability Measures, 2nd edn. Birkhäuser Basel (2008). [Google Scholar]
  18. J.-D. Benamou and Y. Brenier, A computational fluid mechanics solution to the Monge–Kantorovich mass transfer problem. Numer. Math. 84 (2000) 375–393. [Google Scholar]
  19. L.E. Dubins, On extreme points of convex sets. J. Math. Anal. Applic. 5 (1962) 237–244. [CrossRef] [Google Scholar]
  20. L.D. Brown and R. Purves, Measurable selections of extrema. Ann. Statist. (1973) 902–912. [Google Scholar]
  21. C.D. Aliprantis and K.C. Border, Infinite Dimensional Analysis: A Hitchhiker’s Guide, 3rd [rev. and enl.] edn. Springer, Berlin; New York (2006). OCLC: ocm69983226. [Google Scholar]
  22. V.F. Demyanov and A.M. Rubinov, Approximate Methods in Optimization Problems, Vol. 32. Elsevier Publishing Company (1970). [Google Scholar]
  23. M. Frank and P. Wolfe, An algorithm for quadratic programming. Naval Res. Logist. Quart. 3 (1956) 95–110. [CrossRef] [MathSciNet] [Google Scholar]
  24. A. Silveti-Falls, C. Molinari and J. Fadili, Inexact and stochastic generalized conditional gradient with augmented lagrangian and proximal step. arXiv preprint arXiv:2005.05158, 2020. [Google Scholar]
  25. T.H. Cormen, C.E. Leiserson, R.L. Rivest and C. Stein, Introduction to Algorithms, 3rd edn. MIT Press (2009). [Google Scholar]
  26. R.T. Rockafellar, Conjugate Duality and Optimization. SIAM (1974). [CrossRef] [Google Scholar]
  27. L. Chizat, G. Peyré, B. Schmitzer and F.-X. Vialard, Unbalanced optimal transport: Dynamic and Kantorovich formulations. J. Funct. Anal. 274 (2018) 3090–3123. [CrossRef] [MathSciNet] [Google Scholar]
  28. L. Chizat, G. Peyré, B. Schmitzer and F.-X. Vialard, An interpolating distance between optimal transport and Fisher–Rao metrics. Found. Computat. Math. 18 (2018) 1–44. [CrossRef] [Google Scholar]
  29. L. Ding, J. Fan and M. Udell, kFW: a Frank–Wolfe style algorithm with stronger subproblem oracles. arXiv preprint arXiv:2006.16142, 2020. [Google Scholar]
  30. 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. [CrossRef] [MathSciNet] [Google Scholar]
  31. K. Yosida, Functional Analysis, 6th edn. Springer Berlin Heidelberg (1980). [Google Scholar]
  32. V.I. Bogachev, Measure Theory. Springer-Verlag Berlin Heidelberg (2007). [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.