Metric subregularity of order q and the solving of inclusions

Central European Journal of Mathematics - Tập 9 Số 1 - Trang 147-161 - 2011
Michaël Gaydu1, Michel Geoffroy1, Célia Jean-Alexis1
1LAMIA (EA4540), Department of Mathematics, Université des Antilles et de la Guyane, Guadeloupe, France

Tóm tắt

Từ khóa


Tài liệu tham khảo

Alt W., Lipschitzian perturbations of infinite optimization problems, In: Mathematical Programming with Data Perturbations, II, Washington D.C., 1980, Lecture Notes in Pure and Appl. Math., 85, Dekker, New York, 1983, 7–21

Aragón Artacho F.J., Dontchev A.L., Geoffroy M.H., Convergence of the proximal point method for metrically regular mappings, In: CSVAA 2004 — Control Set-Valued Analysis and Applications, ESAIM Proc., 17, EDP Sci., Les Ulis, 2007, 1–8

Aragón Artacho F.J., Geoffroy M.H., Characterization of metric regularity of subdifferentials, J. Convex Anal., 2008, 15(2), 365–380

Azé D., A unified theory for metric regularity of multifunctions, J. Convex Anal., 2006, 13(2), 225–252

Banach S., Théorie des Opérations Linéaires, Monografje Matematyczne, Warsaw, 1932

Borwein J.M., Zhuang D.M., Verifiable necessary and sufficient conditions for openness and regularity of set-valued and single-valued maps, J. Math. Anal. Appl., 1988, 134(2), 441–459

Dontchev A.L., Local analysis of a Newton-type method based on partial linearization, In: The Mathematics of Numerical Analysis, Park City, 1995, Lectures in Appl. Math., 32, AMS, Providence, 1996, 295–306

Dontchev A.L., Rockafellar R.T., Implicit Functions and Solution Mappings, Springer Monogr. Math., Springer, Dordrecht, 2009

Ferris M.C., Pang J.S., Engineering and economic applications of complementarity problems, SIAM Rev., 1997, 39(4), 669–713

Fischer A., Local behavior of an iterative framework for generalized equations with nonisolated solutions, Math. Program., 2002, 94A(1), 91–124

Frankowska H., An open mapping principle for set-valued maps, J. Math. Anal. Appl., 1987, 127(1), 172–180

Frankowska H., Some inverse mapping theorems. Ann. Inst. H. Poincaré Anal. Non Linéaire, 1990, 7(3), 183–234

Frankowska H., Quincampoix M., Hölder Metric Regularity of Set-Valued Maps, Math. Program. (in press), DOI: 10.1007/s10107-010-0401-7

Geoffroy M.H., Jean-Alexis C., Piétrus A., A Hummel-Seebeck type method for variational inclusions, Optimization, 2009, 58(4), 389–399

Geoffroy M.H., Pietrus A., A general iterative procedure for solving nonsmooth generalized equations, Comput. Optim. Appl., 2005, 31(1), 57–67

Henrion R., Outrata J., Surowiec T., Strong stationary solutions to equilibrium problems with equilibrium constraints with applications to an electricity spot market model, preprint available at http://www.matheon.de/preprints/ 5511_sstat.pdf

Ioffe A.D., Metric regularity and subdifferential calculus, Russian Math. Surveys, 2000, 55(3), 501–558

Klatte D., On quantitative stability for non-isolated minima, Control Cybernet., 1994, 23(1–2), 183–200

Kummer B., Inclusions in general spaces: Hoelder stability, solution schemes and Ekeland's principle, J. Math. Anal. Appl., 2009, 358(2), 327–344

Leventhal D., Metric subregularity and the proximal point method, J. Math. Anal. Appl., 2009, 360(2), 681–688

Mordukhovich B.S., Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions, Trans. Amer. Math. Soc., 1993, 340(1), 1–35

Mordukhovich B.S., Variational Analysis and Generalized Differentiation I: Basic Theory, Grundlehren Math. Wiss., 330, Springer, Berlin, 2006

Penot J.-P., Metric regularity, openness and Lipschitzian behavior of multifunctions, Nonlinear Anal., 1989, 13(6), 629–643

Robinson S.M., Generalized equations, In: Mathematical Programming: the State of the Art, Bonn, 1982, Springer, Berlin, 1983, 346–367

Robinson S.M., Newton's method for a class of nonsmooth functions, Set-Valued Anal., 1994, 2(1–2), 291–305

Walras L., Elements of Pure Economics, Alen and Unwin, London, 1954

Wardrop J.G., Some theoritical aspects of road traffic research, In: Proceedings of the Institute of Civil Engineers, Part II, 1952, 325–378

Yen N.D., Yao J.-C., Kien B.T., Covering properties at positive-order rates of multifunctions and some related topics, J. Math. Anal. Appl., 2008, 338(1), 467–478