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All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 1 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 1
Number of page(s) 37
DOI https://doi.org/10.1051/cocv/2024075
Published online 06 January 2025
  1. T.L. Szabo, Diagnostic Ultrasound Imaging: Inside Out. Academic Press (2004). [Google Scholar]
  2. J.E. Kennedy, High-intensity focused ultrasound in the treatment of solid tumours. Nat. Rev. Cancer 5 (2005) 321–327. [CrossRef] [PubMed] [Google Scholar]
  3. G. Allaire, C. Dapogny and F. Jouve, Shape and topology optimization, in Handbook of Numerical Analysis, Vol. 22. Elsevier (2021) 1–132. [Google Scholar]
  4. A. Manzoni, A. Quarteroni and S. Salsa, Optimal Control of Partial Differential Equations. Springer (2021). [CrossRef] [Google Scholar]
  5. C. Clason, K. Kunisch and P. Trautmann, Optimal control of the principal coefficient in a scalar wave equation. Appl. Math. Optim. 84 (2021) 2889–2921. [CrossRef] [MathSciNet] [Google Scholar]
  6. H. Garcke, S. Mitra and V. Nikolić, A phase-field approach to shape and topology optimization of acoustic waves in dissipative media. SIAM J. Control Optim. 60 (2022) 2297–2319. [CrossRef] [MathSciNet] [Google Scholar]
  7. Q.D. Tran, G.-W. Jang, H.-S. Kwon and W.-H. Cho, Shape and topology optimization of acoustic lens system using phase field method. Struct. Multidiscipl. Optim. 56 (2017) 713–729. [CrossRef] [Google Scholar]
  8. X. Hu, Z. Li, R. Bao, W. Chen and H. Wang, An adaptive method of moving asymptotes for topology optimization based on the trust region. Comput. Methods Appl. Mech. Eng. 393 (2022) 114202. [CrossRef] [Google Scholar]
  9. P. Manns and A. Schiemann, On integer optimal control with total variation regularization on multi-dimensional domains. SIAM J. Control Optim. 61 (2023) 3415–3441. [CrossRef] [MathSciNet] [Google Scholar]
  10. X.Y. Yan, Y. Liang and G.D. Cheng, Discrete variable topology optimization for simplified convective heat transfer via sequential approximate integer programming with trust-region. Int. J. Numer. Methods Eng. 122 (2021) 5844–5872. [CrossRef] [Google Scholar]
  11. S. Leyffer and P. Manns, Sequential linear integer programming for integer optimal control with total variation regularization. ESAIM: Control Optim. Calc. Var. 28 (2022) 66. [CrossRef] [EDP Sciences] [Google Scholar]
  12. S. Bartels, Total variation minimization with finite elements: convergence and iterative solution. SIAM J. Numer. Anal. 50 (2012) 1162–1180. [CrossRef] [MathSciNet] [Google Scholar]
  13. C. Caillaud and A. Chambolle, Error estimates for finite differences approximations of the total variation. IMA J. Numer. Anal. (2022) 692–736. [Google Scholar]
  14. A. Chambolle and T. Pock, Approximating the total variation with finite differences or finite elements, in Handbook of Numerical Analysis, Vol. 22. Elsevier (2021) 383–417. [Google Scholar]
  15. S. Amstutz, C. Dapogny and A. Ferrer, A consistent approximation of the total perimeter functional for topology optimization algorithms. ESAIM: Control Optim. Calc. Var. 28 (2022) 1–71. [Google Scholar]
  16. S. Amstutz and N. Van Goethem, Topology optimization methods with gradient-free perimeter approximation. Interfaces Free Bound. 14 (2012) 401–430. [CrossRef] [MathSciNet] [Google Scholar]
  17. F. Maggi, Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory, Vol. 135. Cambridge University Press (2012). [CrossRef] [Google Scholar]
  18. M. Burger, Y. Dong and M. Hintermüller, Exact relaxation for classes of minimization problems with binary constraints, arXiv preprint arXiv:1210.7507 (2012). [Google Scholar]
  19. J. Marko and G. Wachsmuth, Integer optimal control problems with total variation regularization: optimality conditions and fast solution of subproblems. ESAIM: Control Optim. Calc. Var. 29 (2023) 81. [CrossRef] [EDP Sciences] [Google Scholar]
  20. A. Schiemann and P. Manns, Discretization of total variation in optimization with integrality constraints. SIAM J. Numer. Anal. (2024) accepted/to appear. [Google Scholar]
  21. L. Modica, The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal. 98 (1987) 123–142. [CrossRef] [MathSciNet] [Google Scholar]
  22. I. Fonseca and L. Tartar, The gradient theory of phase transitions for systems with two potential wells. Proc. Roy. Soc. Edinb. A Math. 111 (1989) 89–102. [CrossRef] [Google Scholar]
  23. L. Modica and S. Mortola, Un esempio di Γ-convergenca. Bull. Un. Mat. Ital. (1977) 285–299. [Google Scholar]
  24. K. Gröger, A W1,p-estimate for solutions to mixed boundary value problems for second order elliptic differential equations. Math. Ann. 283 (1989) 679–687. [Google Scholar]
  25. C.G. Simader, On Dirichlet’s Boundary Value Problem: Lp-Theory Based on a Generalization of Garding’s Inequality. Vol. 268 of Lecture Notes in Mathematics. Springer (1972). [Google Scholar]
  26. C. Meyer and A. Schiemann, Dual regularization and outer approximation of optimal control problems in BV, submitted (2024). [Google Scholar]
  27. E. Casas and K. Kunisch, Analysis of optimal control problems of semilinear elliptic equations by BV-functions. Set-Valued Var. Anal. 27 (2019) 355–379. [CrossRef] [MathSciNet] [Google Scholar]
  28. K. Bredies, J.A. Iglesias and D. Walter, On extremal points for some vectorial total variation seminorms, arXiv preprint arXiv:2404.12831 (2024) 1–15. [Google Scholar]
  29. M.S. Alnaes, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M.E. Rognes and G.N. Wells, The FEniCS project version 1.5. Arch. Numer. Softw. 3 (2015) 1–15. [Google Scholar]
  30. M.W. Scroggs, I.A. Baratta, C.N. Richardson and G.N. Wells, Basix: a runtime finite element basis evaluation library. J. Open Source Softw. 7 (2022) 3982. [CrossRef] [Google Scholar]
  31. M.W. Scroggs, J.S. Dokken, C.N. Richardson and G.N. Wells, Construction of arbitrary order finite element degree- of-freedom maps on polygonal and polyhedral cell meshes. ACM Trans. Math. Softw. 48 (2022) 18:1–18:23. [CrossRef] [Google Scholar]
  32. A. Meurer, C.P. Smith, M. Paprocki, O. Čertík, S.B. Kirpichev, M. Rocklin, A. Kumar, S. Ivanov, J.K. Moore, S. Singh, T. Rathnayake, S. Vig, B.E. Granger, R.P. Muller, F. Bonazzi, H. Gupta, S. Vats, F. Johansson, F. Pedregosa, M.J. Curry, A.R. Terrel, V. Roučka, A. Saboo, I. Fernando, S. Kulal, R. Cimrman and A. Scopatz, Sympy: symbolic computing in python. PeerJ Comput. Sci. 3 (2017) e103. [CrossRef] [Google Scholar]
  33. P.M. Pardalos and S.A. Vavasis, Quadratic programming with one negative eigenvalue is np-hard. J. Global Optim. 1 (1991) 15–22. [CrossRef] [MathSciNet] [Google Scholar]
  34. Gurobi Optimization, LLC, Gurobi Optimizer Reference Manual (2023). [Google Scholar]
  35. R. Dautray and J.-L. Lions, Evolution problems I, volume 5 of mathematical analysis and numerical methods for science and technology, 1992. [Google Scholar]
  36. L.C. Evans, Partial Differential Equations, Vol. 2. Graduate Studies in Mathematics. AMS (2010). [Google Scholar]
  37. L. Bociu, P. Manns, M. Severitt and S. Strikwerda, Input regularization for integer optimal control in BV with applications to control of poroelastic and poroviscoelastic systems. JNSAO 5 (2024) 1–38. [CrossRef] [Google Scholar]

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