Oriented Calmness and Sweeping Process Dynamics

Published Online:https://doi.org/10.1287/moor.2021.0269

References

  • [1] Bolte J, Daniilidis A, Lewis A (2007) The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems. SIAM J. Optim. 17(4):1205–1223.CrossrefGoogle Scholar
  • [2] Bolte J, Daniilidis A, Lewis A, Shiota M (2007) Clarke subgradients of stratifiable functions. SIAM J. Optim. 18(2):556–572.CrossrefGoogle Scholar
  • [3] Bolte J, Daniilidis A, Ley O, Mazet L (2010) Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity. Trans. Amer. Math. Soc. 362(6):3319–3363.CrossrefGoogle Scholar
  • [4] Cobzas S (2012) Functional Analysis in Asymmetric Normed Spaces (Springer Science & Business Media, Berlin).Google Scholar
  • [5] Colombo G, Goncharov V (1999) The sweeping processes without convexity. Set-Valued Anal. 7:357–374.CrossrefGoogle Scholar
  • [6] Colombo G, Kozaily C (2020) Existence and uniqueness of solutions for an integral perturbation of Moreau’s sweeping process. J. Convex Anal. 27(1):229–238.Google Scholar
  • [7] Daniilidis A, Drusvyatskiy D (2017) Sweeping by a tame process. Ann. Inst. Fourier (Grenoble) 67(5):2201–2223.CrossrefGoogle Scholar
  • [8] Daniilidis A, Supelcre JM, Venegas MF (2021) Asymmetric free spaces and canonical asymmetrizations. Studia Math. 261(1):55–102.CrossrefGoogle Scholar
  • [9] Georgiev B, Ribarska N (2013) On sweeping process with the cone of limiting normals. Set-Valued Variational Anal. 21(4):673–689.CrossrefGoogle Scholar
  • [10] Henrion R, Outrata J (2001) A subdifferential condition for calmness of multifunctions. J. Math. Anal. Appl. 258(1):110–130.CrossrefGoogle Scholar
  • [11] Jourani A, Vilchez E (2016) Positively α-far sets and existence results for generalized perturbed sweeping processes. J. Convex Anal. 23(3):775–821.Google Scholar
  • [12] Kurdyka K (1998) On gradients of functions definable in o-minimal structures. Ann. Inst. Fourier (Grenoble) 48(3):769–783.CrossrefGoogle Scholar
  • [13] Łojasiewicz S (1963) Une propriété topologique des sous-ensembles analytiques réels. Colloques Internationaux du CNRS. Les Equations aux Dérivées Partielles, vol. 117, ed. B (Publications du CNRS, Paris).Google Scholar
  • [14] Łojasiewicz S (1984) Sur les trajectoires du gradient d’une fonction analytique. Seminari di Geometria (Università degli Studi di Bologna, Bologna, Italy), 115–117.Google Scholar
  • [15] Moreau JJ (1971) Rafle par un convexe variable. I. Travaux du Séminaire d’Analyse Convexe, vol. I, no. 15, Secrétariat des Math., no. 118 (University of Science and Techniques of Languedoc, Montpellier, France).Google Scholar
  • [16] Palis J, de Melo W (1982) Geometric Theory of Dynamical Systems (Springer-Verlag, New York).CrossrefGoogle Scholar
  • [17] Rockafellar T, Wets R (1998) Variational Analysis, 2nd ed. (Springer-Verlag, Berlin Heidelberg).CrossrefGoogle Scholar
  • [18] van den Dries L (1998) Tame Topology and o-Minimal Structures, London Mathematical Society Lecture Note Series 248 (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.