Metric subregularity of order q and the solving of inclusions
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