Variational inequalities over perturbed polyhedral convex sets

Mathematics of Operations Research

Volumn 33, Issue 3, 2008, Pages 689-711

  Lu, Shu ^a   Robinson, Stephen M ^b  

^a University of North Carolina at Chapel Hill   (United States)

^b University of Wisconsin Madison   (United States)

Author keywords

Coherent orientation; Normal manifold; Polyhedral convex set; Polyhedral multifunction; Sensitivity; Variational inequality

Indexed keywords

COHERENT ORIENTATION; NORMAL MANIFOLD; POLYHEDRAL CONVEX SET; POLYHEDRAL MULTIFUNCTION; SENSITIVITY; VARIATIONAL INEQUALITY;

VARIATIONAL TECHNIQUES;

SET THEORY;

EID: 61349144374     PISSN: 0364765X     EISSN: 15265471     Source Type: Journal    
DOI: 10.1287/moor.1070.0297     Document Type: Article

References (25)

1. Böhm, V. 1975. On the continuity of the optimal policy set for linear programs. SIAM J. Appl. Math. 28 303-306.
2. Cottle, R. W., J.-S. Pang, R. E. Stone. 1992. The Linear Complementarity Problem. Academic Press, Inc., Boston, MA.
3. Dontchev, A. L., R. T. Rockafellar. 1996. Characterizations of strong regularity for variational inequalities over polyhedral convex sets. SIAM J. Optim. 6 1087-1105.
4. Facchinei, F., J.-S. Pang. 2003. Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer Series in Operations Research, Springer-Verlag, New York. Published in two volumes, paginated continuously.
5. Fujisawa, T., E. S. Kuh. 1972. Piecewise-linear theory of nonlinear networks. SIAM J. Appl. Math. 22(2) 307-328.
6. Householder, A. S. 1975. The Theory of Matrices in Numerical Analysis. Dover Publications, Mineola, NY. Originally published 1964 by Blaisdell Publishing Co.
7. Klatte, D., B. Kummer. 2005. Strong Lipschitz stability of stationary solutions for nonlinear programs and variational inequalities. SIAM J. Optim. 16 96-119.
8. - = y. Linear Algebra Its Appl. 96 109-129.
9. Luo, Z.-Q., J.-S. Pang, D. Ralph. 1996. Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge, UK.
10. Mangasarian, O. L., T.-H. Shiau. 1987. Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems. SIAM J. Control Optim. 25 583-595.
11. Ralph, D. 1993. A new proof of Robinson's homeomorphism theorem for PL-normal maps. Linear Algebra Its Appl. 178 249-260.
12. Ralph, D. 1994. On branching numbers of normal manifolds. Nonlinear Anal.: Theory, Methods, Appl. 22 1041-1050.
13. Robinson, S. M. 1980. Strongly regular generalized equations. Math. Oper. Res. 5 43-62.
14. Robinson, S. M. 1991. An implicit-function theorem for a class of nonsmooth functions. Math. Oper. Res. 16 292-309.
15. Robinson, S. M. 1992. Normal maps induced by linear transformations. Math. Oper. Res. 17 691-714.
16. Robinson, S. M. 1995. Sensitivity analysis of variational inequalities by normal-map techniques. F. Giannessi, A. Maugeri, eds. Variational Inequalities and Network Equilibrium Problems. Plenum. Press, New York, 257-269.
17. Robinson, S. M. 2003. Variational conditions with smooth constraints: Structure and analysis. Math. Programming Ser. B 97 245-265.
18. Robinson, S. M. 2004. Localized normal maps and the stability of variational conditions. Set-Valued Anal. 12 259-274.
19. Robinson, S. M. 2006. Errata to 'Localized normal maps and the stability of variational conditions' (Set-Valued Anal. 12 (2004), 259-274). Set-Valued Anal. 14 207.
20. Robinson, S. M. 2007. Solution continuity in monotone affine variational inequalities. SIAM J. Optim. 18 1046-1060.
21. Rockafellar, R. T. 1970. Convex Analysis. Princeton University Press, Princeton, NJ.
22. Rockafellar, R. T, R. J-B. Wets. 1998. Variational Analysis. Grundlehren der mathematischen Wissenschaften, Vol. 317, Springer-Verlag, Berlin, Germany.
23. Scholtes, S. 1994. Introduction to piecewise differentiable equations. Habilitation thesis (Habilitationsschrift), Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Karlsruhe, Germany.
24. Scholtes, S. 1996. A proof of the branching number bound for normal manifolds. Linear Algebra Its Appl. 246 83-95.
25. Yen, N. D. 1995. Lipschitz continuity of solutions of variational inequalities with a parametric polyhedral constraint. Math. Oper. Res. 20 695-708.