Open Access
Volume 26, 2020
Article Number 90
Number of page(s) 45
Published online 16 November 2020
  1. P.-A. Absil and J. Malick, Projection-like retractions on matrix manifolds. SIAM J. Optim. 22 (2012) 135–158. [Google Scholar]
  2. P.-A. Absil, R. Mahony and R. Sepulchre, Optimization algorithms on matrix manifolds. Princeton University Press, Princeton (2009). [Google Scholar]
  3. G. Allaire, Conception optimale de structures, Vol. 58 of Mathématiques & Applications. Springer-Verlag, Berlin (2007). [Google Scholar]
  4. G. Allaire and F. Jouve, Minimum stress optimal design with the level set method. Eng. Anal. Bound. Elements 32 (2008) 909–918. [CrossRef] [Google Scholar]
  5. G. Allaire and O. Pantz, Structural optimization with freefem++. Struct. Multidiscipl. Optim. 32 (2006) 173–181. [Google Scholar]
  6. G. Allaire, F. Jouve and A.-M. Toader, Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194 (2004) 363–393. [Google Scholar]
  7. G. Allaire, C. Dapogny and P. Frey, Shape optimization with a level set based mesh evolution method. Comput. Methods Appl. Mech. Eng. 282 (2014) 22–53. [Google Scholar]
  8. G. Allaire, F. Jouve and G. Michailidis, Casting constraints in structural optimization via a level-set method, in 10th world Congress on Structural and Multidisciplinary Optimization (2013). [Google Scholar]
  9. G. Allaire, F. Jouve and G. Michailidis, Thickness control in structural optimization via a level set method. Struct. Multidiscipl. Optim. 53 (2016) 1349–1382. [Google Scholar]
  10. G. Allaire, C. Dapogny, R. Estevez, A. Faure and G. Michailidis, Structural optimization under overhang constraints imposed by additive manufacturing technologies. J. Comput. Phys. 351 (2017) 295–328. [Google Scholar]
  11. L. Ambrosio, M. Colombo and A. Figalli, Existence and uniqueness of maximal regular flows for non-smooth vector fields. Arch. Ration. Mech. Anal. 218 (2015) 1043–1081. [Google Scholar]
  12. M. Andersen, J. Dahl and L. Vandenberghe, CVXOPT: A Python package for convex optimization Available at (2012). [Google Scholar]
  13. S. Arguillère, E. Trélat, A. Trouvé and L. Younes, Shape deformation analysis from the optimal control viewpoint. J. Math. Pures Appl. 104 (2015) 139–178. [Google Scholar]
  14. H. Azegami and Z.C. Wu, Domain optimization analysis in linear elastic problems: approach using traction method. JSME Int. J. Ser. A, Mech. Mater. Eng. 39 (1996) 272–278. [Google Scholar]
  15. C. Barbarosie and S. Lopes, A gradient-type algorithm for optimization with constraints, submitted for publication, see also Pre-PrintCMAF Pre-2011-001 at (2011). [Google Scholar]
  16. C. Barbarosie, A.-M. Toader and S. Lopes, A gradient-type algorithm for constrained optimization with application to microstructure optimization. Discr. Cont. Dyn. Syst. B 22 (2020) 1729–1755. [Google Scholar]
  17. J.-F. Bonnans, J.C. Gilbert, C. Lemaréchal and C.A. Sagastizábal, Numerical optimization: theoretical and practical aspects. Springer Science & Business Media, Berlin (2006). [Google Scholar]
  18. H. Brezis, Functional analysis, Sobolev spaces and partial differential equations. Springer Science & Business Media, Berlin (2010). [CrossRef] [Google Scholar]
  19. R. Bro and S. De Jong A fast non-negativity-constrained least squares algorithm. J. Chemometr. 11 (1997) 393–401. [CrossRef] [Google Scholar]
  20. C. Bui, C. Dapogny and P. Frey, An accurate anisotropic adaptation method for solving the level set advection equation. Int. J. Num. Methods Fluids 70 (2012) 899–922. [CrossRef] [Google Scholar]
  21. M. Burger, A framework for the construction of level set methods for shape optimization and reconstruction. Interfaces Free Bound. 5 (2003) 301–329. [CrossRef] [MathSciNet] [Google Scholar]
  22. C. Dapogny, C. Dobrzynski and P. Frey, Three-dimensional adaptive domain remeshing, implicit domain meshing, and applications to free and moving boundary problems. J. Comput. Phys. 262 (2014) 358–378. [Google Scholar]
  23. C. Dapogny, P. Frey, F. Omnès and Y. Privat, Geometrical shape optimization in fluid mechanics using FreeFem++, in Structural and Multidisciplinary Optimization. Springer, Germany (2017) 1–28. [Google Scholar]
  24. F. De Gournay Velocity extension for the level-set method and multiple eigenvalues in shape optimization. SIAM J. Control Optim. 45 (2006) 343–367. [Google Scholar]
  25. L. Dieci and L. Lopez, A survey of numerical methods for ivps of odes with discontinuous right-hand side. J. Comput. Appl. Math. 236 (2012) 3967–3991. [Google Scholar]
  26. J. Dieudonné, Foundations of modern analysis. Academic press, New York (1960). [Google Scholar]
  27. P.D. Dunning and H.A. Kim, Introducing the sequential linear programming level-set method for topology optimization. Struct. Multidiscipl. Optim. 51 (2015) 631–643. [Google Scholar]
  28. P. Duysinx and M.P. Bendsøe, Topology optimization of continuum structures with local stress constraints. Int. J. Numer. Methods Eng. 43 (1998) 1453–1478. [Google Scholar]
  29. A. Edelman, T.A. Arias and S.T. Smith, The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20 (1998) 303–353. [Google Scholar]
  30. A. Faure, Optimisation de forme de matériaux et structures architecturés par la méthode des lignes de niveaux avec prise en compte des interfaces graduées. Ph.D. thesis, Grenoble Alpes (2017). [Google Scholar]
  31. F. Feppon, Shape and topology optimization of multiphysics systems. Ph.D. thesis, Thèse de doctorat de l’Université Paris Saclay préparée à l’Écolepolytechnique (2019). [Google Scholar]
  32. F. Feppon, G. Allaire, F. Bordeu, J. Cortial and C. Dapogny, Shape optimization of a coupled thermal fluid-structure problem in a level set mesh evolution framework. SerMA J. 76 (2019) 413–458. [Google Scholar]
  33. A.F. Filippov, Differential equations with discontinuous righthand sides: control systems. Vol. 18. Springer Science & Business Media, Berlin (2013). [Google Scholar]
  34. R. Fletcher, Practical methods of optimization. John Wiley & Sons, New Jersey (2013). [Google Scholar]
  35. A. Henrot and M. Pierre, Shape variation and optimization, A geometrical analysis. English version of the French publication [MR2512810] with additions and updates. Vol. 28 of EMS Tracts in Mathematics, European Mathematical Society (EMS). Zürich (2018). [Google Scholar]
  36. M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semismooth newton method. SIAM J. Optim. 13 (2002) 865–888. [Google Scholar]
  37. H.T. Jongen and O. Stein, On the complexity of equalizing inequalities. J. Global Optim. 27 (2003) 367–374. [CrossRef] [Google Scholar]
  38. H.T. Jongen and O. Stein, Constrained global optimization: adaptive gradient flows, in Frontiers in global optimization, Vol. 74 of Nonconvex Optimization and its Application. Kluwer Academic Publishing, Boston, MA (2004) 223–236. [CrossRef] [Google Scholar]
  39. J. Jost, Chapter 7 Morse Theory and Floer Homology. Springer Berlin Heidelberg (2011) 327–417. [Google Scholar]
  40. C. Le, J. Norato, T. Bruns, C. Ha and D. Tortorelli, Stress-based topology optimization for continua. Struct. Multidiscipl. Optim. 41 (2010) 605–620. [Google Scholar]
  41. J.D. Lee, M. Simchowitz, M.I. Jordan and B. Recht, Gradient descent only converges to minimizers, in 29th Annual Conference on Learning Theory. Edited by V. Feldman, A. Rakhlin and O. Shamir. Vol. 49 of Proceedings of Machine Learning Research Columbia University, New York, USA (2016) 1246–1257. [Google Scholar]
  42. J. Liu and Y. Ma, A survey of manufacturing oriented topology optimization methods. Adv. Eng. Softw. 100 (2016) 161–175. [Google Scholar]
  43. L. Ljung, Analysis of recursive stochastic algorithms. IEEE Trans. Autom. Control 22 (1977) 551–575. [CrossRef] [Google Scholar]
  44. D.G. Luenberger, The gradient projection method along geodesics. Manag. Sci. 18 (1972) 620–631. [CrossRef] [Google Scholar]
  45. B. Mohammadi and O. Pironneau, Applied shape optimization for fluids. Oxford University Press, Oxford (2010). [Google Scholar]
  46. P. Morin, R. Nochetto, M. Pauletti and M. Verani, Adaptive sqp method for shape optimization, in Numerical Mathematics and Advanced Applications 2009. Springer, Berlin (2010) 663–673. [CrossRef] [Google Scholar]
  47. F. Murat and J. Simon, Sur le contrôle par un domaine géométrique, publications du Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie (1976). [Google Scholar]
  48. J. Nocedal and S.J. Wright, Numerical optimization. Springer Science, Berlin (1999) 35. [Google Scholar]
  49. S. Osher and J.A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on hamilton-jacobi formulations. J. Comput. Phys. 79 (1988) 12–49. [Google Scholar]
  50. I. Panageas and G. Piliouras, Gradient descent only converges to minimizers: Non-isolated critical points and invariant regions. Preprint arXiv:1605.00405 (2016). [Google Scholar]
  51. J. Schropp and I. Singer, A dynamical systems approach to constrained minimization. Numer. Funct. Anal. Optim. 21 (2000) 537–551. [Google Scholar]
  52. V.H. Schulz, A Riemannian view on shape optimization. Found. Comput. Math. 14 (2014) 483–501. [CrossRef] [MathSciNet] [Google Scholar]
  53. V.H. Schulz, M. Siebenborn and K. Welker, Efficient pde constrained shape optimization based on steklov–poincaré-type metrics. SIAM J. Optim. 26 (2016) 2800–2819. [Google Scholar]
  54. V. Shikhman and O. Stein, Constrained optimization: projected gradient flows. J. Optim. Theory Appl. 140 (2009) 117–130. [Google Scholar]
  55. O. Sigmund, Manufacturing tolerant topology optimization. Acta Mech. Sinica 25 (2009) 227–239. [CrossRef] [Google Scholar]
  56. J. Sokolowski and J.-P. Zolesio, Introduction to shape optimization, in Introduction to Shape Optimization. Springer, Berlin (1992) 5–12. [CrossRef] [Google Scholar]
  57. J. Sokolowski and J.-P. Zolésio, Introduction to shape optimization. Vol. 16 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (1992). [CrossRef] [Google Scholar]
  58. K. Svanberg, The method of moving asymptotes—a new method for structural optimization. Int. J. Numer. Methods Eng. 24 (1987) 359–373. [Google Scholar]
  59. K. Tanabe, A geometric method in nonlinear programming. J. Optim. Theory Appl. 30 (1980) 181–210. [Google Scholar]
  60. G.N. Vanderplaats and F. Moses, Structural optimization by methods of feasible directions. Comput. Struct. 3 (1973) 739–755. [Google Scholar]
  61. A. Wächter and L.T. Biegler, On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106 (2006) 25–57. [Google Scholar]
  62. M.Y. Wang, X. Wang and D. Guo, A level set method for structural topology optimization. Comput. Methods Appl. Mech. Eng. 192 (2003) 227–246. [Google Scholar]
  63. Q. Xia and M.Y. Wang, Topology optimization of thermoelastic structures using level set method. Comput. Mech. 42 (2008) 837–857. [Google Scholar]
  64. Q. Xia, T. Shi, M. Y. Wang and S. Liu, A level set based method for the optimization of cast part. Struct. Multidiscipl. Optim. 41 (2010) 735–747. [Google Scholar]
  65. H. Yamashita, A differential equation approach to nonlinear programming. Math. Program. 18 (1980) 155–168. [Google Scholar]
  66. Y.-X. Yuan, A review of trust region algorithms for optimization. ICIAM 99 (2000) 271–282. [Google Scholar]
  67. M. Yulin and W. Xiaoming, A level set method for structural topology optimization with multi-constraints and multi-materials. Acta Mech. Sin. 20 (2004) 507–518. [Google Scholar]
  68. G. Zoutendijk, Methods of feasible directions: A study in linear and non-linear programming. Elsevier Publishing Co., Amsterdam (1960). [Google Scholar]

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