On the coderivative of the projection operator onto the second-order cone

Set-Valued Analysis

Volumn 16, Issue 7-8, 2008, Pages 999-1014

  Outrata, Jiří V ^a   Sun, Defeng ^b  

^a INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Aubin property; Limiting coderivative; Projection; Second order cone

Indexed keywords

EID: 58149165329     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11228-008-0092-x     Document Type: Article

References (21)

1. J.-P. Aubin 1984 Lipschitz behaviour of solutions to convex minimization problems Math. Oper. Res. 9 87 111
2. J.-S. Chen X. Chen P. Tseng 2004 Analysis of nonsmooth vector-valued functions associated with second-order cones Math. Programming 101 95 117
3. X.-D. Chen D. Sun J. Sun 2003 Complementarity functions and numerical experiments for second-order cone complementarity problems Comput. Optim. Appl. 25 39 56
4. Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)
5. Faraut, U., Korányi, A.: Analysis on Symmetric Cones. Oxford Mathematical Monographs. Oxford University Press, New York (1994)
6. M. Fukushima Z.-Q. Luo P. Tseng 2002 Smoothing functions for second-order cone complementarity problems SIAM J. Optim. 12 436 460
7. Kanzow, C., Ferenzi, I., Fukushima, M.: Semismooth methods for linear and nonlinear second-order cone programs. Technical Report 2006-005, Department of Applied Mathematics and Physics, Kyoto University (April 2006, revised January 2007).
8. J. Haslinger T. Sassi 2004 Mixed finite element approximation of 3D contact problems with given friction: error analysis and numerical realization Math. Model. Numer. Anal. 38 563 578
9. Koecher, M.: In: Brieg, A., Walcher, S. (eds.) The Minnesota Notes on Jordan Algebras and Their Applications. Springer, Berlin (1999)
10. A. Korányi 1984 Monotone functions on formally real Jordan algebras Math. Ann. 269 73 76
11. Liu, Y.-J., Zhang, L.-W.: Convergence of the augmented Lagrangian method for nonlinear optimization problems over second-order cones. J. Optim. Theory Appl. (2008, in press)
12. M.S. Lobo L. Vandenberghe S. Boyd H. Lebret 1998 Application of second-order cone programming Linear Algebra Appl. 284 193 228
13. B.S. Mordukhovich 1984 Nonsmooth analysis with nonconvex generalized differentials and adjoint mappings Dokl. Akad. Nauk SSSR 28 976 979
14. Mordukhovich, B.S.: Approximation Methods in Problems of Optimization and Control (in Russian). Nauka, Moscow (1988)
15. B.S. Mordukhovich 1994 Generalized differential calculus for nonsmooth and set-valued mappings J. Math. Anal. Appl. 183 250 288
16. Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, vol. 1. Springer, New York (2006)
17. J.S. Pang D.F. Sun J. Sun 2003 Semismooth homeomorphisms and strong stability of semidefinite and Lorentz cone complementarity problems Math. Oper. Res. 28 39 63
18. S.M. Robinson 1980 Strongly regular generalized equation Math. Oper. Res. 5 43 62
19. Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, New York (1998)
20. H. Scheel S. Scholtes 2000 Mathematical programs with complementarity constraints: stationarity, optimality and sensitivity Math. Oper. Res. 25 1 22
21. A. Shapiro 1990 On concepts of directional differentiability J. Optim. Theory Appl. 66 477 487