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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 6
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Articles

Metric regularity of a positive order for generalized equations

Pages 1270-1287 | Received 08 Jul 2013, Accepted 27 May 2014, Published online: 02 Jul 2014

References

  • Dontchev AL, Rockafellar RT. Regularity and conditioning of solution mappings in variational analysis. Set-Valued Anal. 2004;12:79–109.
  • Zheng XY, Ng KF. Metric subregularity and calmness for nonconvex generalized equations in Banach spaces. SIAM J. Optim. 2010;20:2119–2136.
  • Apetrii M, Durea M, Strugariu R. On subregularity properties of set-valued mappings applications to solid vector optimization. Set-Valued Var. Anal. 2013;21:93–126.
  • Bonnans JF, Shapiro A. Perturbation analysis of optimization problems. New York (NY): Springer; 2000.
  • Chuong TD, Kruger AY, Yao J-C. Calmness of efficient solution maps in parametric vector optimization. J. Global Optim. 2011;51:677–688.
  • Dontchev AL, Rockafellar RT. Implicit functions and solution mappings. Springer monographs in mathematics. Dordrecht: Springer; 2009.
  • Gfrerer H. First order and second order characterizations of metric subregularity and calmness of constraint set mappings. SIAM J. Optim. 2011;21:1439–1474.
  • Kummer B. Inclusions in general spaces: Hoelder stability, solution schemes and Ekeland’s principle. J. Math. Anal. Appl. 2009;358:327–344.
  • Leventhal D. Metric subregularity and the proximal point method. J. Math. Anal. Appl. 2009;360:681–688.
  • Rockafellar RT, Wets RJ-B. Variational analysis. Berlin: Springer; 1998.
  • Zheng XY, Ng KF. Metric subregularity for proximal generalized equations in Hilbert spaces. Nonlinear Anal. 2012;75:1686–1699.
  • Mordukhovich BS. Variational analysis and generalized differentiation. I: basic theory. Berlin: Springer; 2006.
  • Frankowska H, Quincampoix M. Hölder metric regularity of set-valued maps. Math. Prog. Ser. A. 2012;132:333–354.
  • Yen ND, Yao J-C, Kien BT. Covering properties at positive-order rates of multifunctions and some related topics. J. Math. Anal. Appl. 2008;338:467–478.
  • Gaydu M, Geoffroy MH, Jean-Alexis C. Metric subregularity of order q and the solving of inclusions. Cent. Eur. J. Math. 2011;9:147–161.
  • Ekeland I. On the variational principle. J. Math. Anal. Appl. 1974;47:324–353.
  • Clarke FH. Optimization and nonsmooth analysis. New York (NY): Wiley; 1983.
  • Li G, Mordukhovich BS. Hölder metric subregularity with applications to proximal point method. SIAM J. Optim. 2012;22:1655–1684.
  • Aubin J-P, Frankowska H. Set-valued analysis. Berlin: Birkhauser; 1990.
  • Fabian M. Subdifferentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss. Acta Univ. Carolin. Math. Phys. 1989;30:51–56.
  • Ngai HV, Thera M. Error bounds for systems of lower semicontinuous functions in Asplund spaces. Math. Prog. Ser. B. 2009;116:397–427.
  • Chuong TD, Kim DS. Hölder-like property and metric regularity of a positive-order for implicit multifunctions. Math. Oper. Res. Forthcoming.
  • Ioffe AD, Tihomirov VM. Theory of extremal problems. Amsterdam (NY): North-Holland Publishing; 1979.

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