Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T07:06:03.307Z Has data issue: false hasContentIssue false
  • English
  • Français

REGULARITY PROPERTIES IN VARIATIONAL ANALYSIS AND APPLICATIONS IN OPTIMISATION

Part of: Existence theories

Published online by Cambridge University Press:  01 April 2016

N. H. THAO
N. H. THAO*
Affiliation:
Institute for Numerical and Applied Mathematics, 16–18 Lotzestrasse, Gottingen 37083, Germany email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'

Keywords

variational analysisconvergence analysisoptimisationstability analysis

MSC classification

Primary: 49J53: Set-valued and variational analysis
Secondary: 65K10: Optimization and variational techniques 90C31: Sensitivity, stability, parametric optimization
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 3 , June 2016 , pp. 523 - 524
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Anh, L. Q. and Khanh, P. Q., ‘On the Hölder continuity of solutions to parametric multivalued vector equilibrium problems’, J. Math. Anal. Appl. 321 (2006), 308–315.Google Scholar
Anh, L. Q., Kruger, A. Y. and Thao, N. H., ‘On Hölder calmness of solution mappings in parametric equilibrium problems’, TOP 22 (2014), 331–342.CrossRefGoogle Scholar
Bauschke, H. H. and Borwein, J. M., ‘On projection algorithms for solving convex feasibility problems’, SIAM Rev. 38 (1996), 367–426.CrossRefGoogle Scholar
Bauschke, H. H. and Combettes, P. L., Convex Analysis and Monotone Operator Theory in Hilbert Spaces (Springer, New York, 2011).CrossRefGoogle Scholar
Dontchev, A. L. and Rockafellar, R. T., Implicit Functions and Solution Mappings. A View from Variational Analysis, Springer Monographs in Mathematics (Springer, Dordrecht, 2009).CrossRefGoogle Scholar
Drusvyatskiy, D., Ioffe, A. D. and Lewis, A. S., ‘Transversality and alternating projections for nonconvex sets’, Found. Comput. Math. 15 (2015), 1637–1651.Google Scholar
Hesse, R. and Luke, D. R., ‘Nonconvex notions of regularity and convergence of fundamental algorithms for feasibility problems’, SIAM J. Optim. 23 (2013), 2397–2419.CrossRefGoogle Scholar
Ioffe, A. D., ‘Metric regularity and subdifferential calculus’, Russian Math. Surveys 55 (2000), 501–558.Google Scholar
Ioffe, A. D., ‘On regularity concepts in variational analysis’, J. Fixed Point Theory Appl. 8 (2010), 339–363.Google Scholar
Ioffe, A. D., ‘Regularity on a fixed set’, SIAM J. Optim. 21 (2011), 1345–1370.CrossRefGoogle Scholar
Ioffe, A. D., ‘Nonlinear regularity models’, Math. Program. 139 (2013), 223–242.Google Scholar
Khanh, P. Q., Kruger, A. Y. and Thao, N. H., ‘An induction theorem and nonlinear regularity models’, SIAM J. Optim. 25 (2015), 2561–2588.CrossRefGoogle Scholar
Kruger, A. Y., ‘About regularity of collections of sets’, Set-Valued Anal. 14 (2006), 187–206.Google Scholar
Kruger, A. Y., ‘About stationarity and regularity in variational analysis’, Taiwanese J. Math. 13 (2009), 1737–1785.CrossRefGoogle Scholar
Kruger, A. Y. and Thao, N. H., ‘About uniform regularity of collections of sets’, Serdica Math. J. 39 (2013), 287–312.Google Scholar
Kruger, A. Y. and Thao, N. H., ‘About [q]-regularity properties of collections of sets’, J. Math. Anal. Appl. 416 (2014), 471–496.Google Scholar
Kruger, A. Y. and Thao, N. H., ‘Quantitative characterizations of regularity properties of collections of sets’, J. Optim. Theory Appl. 164 (2015), 41–67.CrossRefGoogle Scholar
Kruger, A. Y. and Thao, N. H., ‘Regularity of collections of sets and convergence of inexact alternating projections’, J. Convex Anal. 23 (2016), to appear.Google Scholar
Lewis, A. S., Luke, D. R. and Malick, J., ‘Local linear convergence of alternating and averaged projections’, Found. Comput. Math. 9 (2009), 485–513.CrossRefGoogle Scholar
Lewis, A. S. and Malick, J., ‘Alternating projections on manifolds’, Math. Oper. Res. 33 (2008), 216–234.Google Scholar
Mordukhovich, B. S., Variational Analysis and Generalized Differentiation, I: Basic Theory; II: Applications, Grundlehren der mathematischen Wissenschaften (Springer, New York, 2006).Google Scholar
Noll, D. and Rondepierre, A., ‘On local convergence of the method of alternating projections’, Found. Comput. Math. (2015), doi:10.1007/s10208-015-9253-0.Google Scholar
Rockafellar, R. T. and Wets, R. J., Variational Analysis, Grundlehren der mathematischen Wissenschaften (Springer, Berlin, 1998).Google Scholar