Continuity of the solution map in parametric affine variational inequalities

Set-Valued Analysis

Volumn 15, Issue 2, 2007, Pages 105-123

  Lee, Gue Myung ^a   Nang Tam, Nguyen ^b   Yen, Nguyen Dong ^c  

^a Pukyong National University   (South Korea)

^b Hanoi Pedagogical Institute No 2   (Viet Nam)

^c INSTITUTE OF MATHEMATICS   (Viet Nam)

Author keywords

Lagrange multiplier; Lower semicontinuity; Parametric affine variational inequality; Solution map; Upper semicontinuity

Indexed keywords

EID: 34247866211     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11228-006-0039-z     Document Type: Article

References (26)

1. Aubin, J.-P.: Lipschitz behavior of solutions to convex minimization problems. Math. Oper. Res. 9, 87-111 (1984)
2. Aubin, J.-P., Frankowska, H.: Set-Valued Analysis. Birkhäuser, Berlin (1990)
3. Bank, B., Guddat, J., Klatte, D., Kummer, B., Tammer, K.: Non-Linear Parametric Optimization. Akademie-Verlag, Berlin (1982)
4. e tirage. Masson, Paris (1987)
5. Cottle, R.W., Pang, J.-S., Stone, R.E.: The Linear Complementarity Problem. Academic, New York (1992)
6. Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, Vol. I, II. Springer, Berlin Heidelberg New York (2003)
7. Gowda, M.S.: On the continuity of the solution map in linear complementarity problems. SIAM J. Optim. 2, 619-634 (1992)
8. Gowda, M.S., Pang, J.-S.: On the boundedness and stability of solutions to the affine variational inequality problem. SIAM J. Control Optim. 32, 421-441 (1994)
9. Gowda, M.S., Pang, J.-S.: Stability analysis of variational inequalities and nonlinear complementarity problems, via the mixed linear complementarity problem and degree theory. Math. Oper. Res. 19, 831-879 (1994)
10. Gowda, M.S., Sznajder, R.: On the Lipschitzian properties of polyhedral multifunctions. Math. Programming 74, 267-278 (1996)
11. Jansen, M.J.M., Tijs, S.H.: Robustness and nondegenerateness for linear complementarity problems. Math. Programming 37, 293-308 (1987)
12. Lee, G.M., Tam, N.N., Yen, N.D.: Continuity of the solution map in quadratic programs under linear perturbations. (To appear in Journal of Optimization Theory and Applications)
13. Lee, G.M., Tam, N.N., Yen, N.D.: Lower semicontinuity of the KKT point set in quadratic programs under linear perturbations. (To appear in Vietnam Journal of Mathematics)
14. Mangasarian, O.L., Shiau, T.H.: Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems. SIAM J. Control Optim. 25, 583-595 (1987)
15. Oettli, W., Yen, N.D.: Continuity of the solution set of homogeneous equilibrium problems and linear complementarity problems, In: Giannessi, F., Maugeri, A. (eds.) Variational Inequalities and Network Equilibrium Problems, pp. 225-234. Plenum Press, New York (1995)
16. Robinson, S.M.: Stability theory for systems of inequalities, Part I: Linear systems. SIAM J. Numer. Anal. 12, 754-769 (1975)
17. Robinson, S.M.: A characterization of stability in linear programming. Oper. Res. 25, 435-477 (1977)
18. Robinson, S.M.: Generalized equations and their solutions, Part I: Basic theory. Math. Program. Stud. 10, 128-141 (1979)
19. Robinson, S.M.: Strongly regular generalized equations. Math. Oper. Res. 5, 43-62 (1980)
20. Robinson, S.M.: Some continuity properties of polyhedral multifunctions. Math. Program. Stud. 14, 206-214 (1981)
21. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton, N.J. (1970)
22. Tam, N.N.: Sufficient conditions for the stability of the Karush-Kuhn-Tucker point set in quadratic programming. Optimization 50, 45-60 (2001)
23. Tam, N.N.: Continuity of the optimal value function in indefinite quadratic programming. J. Global Optim. 23, 43-61 (2002)
24. Tam, N.N., Yen, N.D.: Continuity properties of the Karush-Kuhn-Tucker point set in quadratic programming problems. Math. Programming 85, 193-206 (1999)
25. Tam, N.N., Yen, N.D.: Stability of the Karush-Kuhn-Tucker point set in a general quadratic programming problem. Vietnam J. Math. 28, 33-45 (2000)
26. Yen, N.D.: Implicit function theorems for set-valued maps. Acta Math. Vietnam. 12(2), 7-28 (1987)