On the identification of degenerate indices in the nonlinear complementarity problem with the proximal point algorithm

Mathematical Programming

Volumn 99, Issue 2, 2004, Pages 377-397

  Yamashita, Nobuo ^a   Dan, Hiroshige ^a,b   Fukushima, Masao ^a  

^a KYOTO UNIVERSITY   (Japan)

^b Mathematical Systems Inc   (Japan)

Author keywords

Degeneracy; Nonlinear complementarity problem; Proximal point algorithm

Indexed keywords

ALGORITHMS; MATHEMATICAL MODELS; OPTIMIZATION; PARAMETER ESTIMATION; PERTURBATION TECHNIQUES; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

DEGENERACY; DEGENERATE INDICES; NONLINEAR COMPLEMENTARITY PROBLEMS; PROXIMAL POINT ALGORITHMS;

NONLINEAR PROGRAMMING;

EID: 21044449922     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-003-0455-x     Document Type: Article

References (19)

1. Billups, S.C.: Improving the robustness of descent-based methods for semismooth equations using proximal perturbations. Math. Program. 87, 269-284 (2000)
2. Bongartz, I., Conn, A.R., Gould, N., Toint, Ph.L.: CUTE: Constrained and unconstrained testing environment. ACM Trans. Math. Softw. 21, 123-160 (1995)
3. El-Bakry, A.S., Tapia, R.A., Zhang, Y.: A study of indicators for identifying zero variables in interior-point methods. SIAM Rev. 36, 45-72 (1994)
4. El-Bakry, A.S., Tapia, R.A., Zhang, Y.: On the convergence rate of Newton interior-point methods in the absence of strict complementarity. Comput. Optim. Appl. 6, 157-167 (1996)
5. De Luca, T., Facchinei, F., Kanzow, C.: A semismooth equation approach to the solution of nonlinear complementarity problems. Math. Program. 75, 407-439 (1996)
6. Facchinei, F., Fischer, A., Kanzow, C.: On the accurate identification of active constraints. SIAM J. Optim. 9, 14-32 (1998)
7. Facchinei, F., Fischer, A., Kanzow, C.: On the identification of zero variables in an interior-point framework. SIAM J. Optim. 10, 1058-1078 (2000)
8. Fischer, A.: A special Newton-type optimization method. Optimization 24, 153-176 (1992)
9. Fischer, A.: An NCP-function and its use for the solution of complementarity problems. In: Du, D.Z., Qi, L., Womersley, R.S. (eds.), Recent Advances in Nonsmooth Optimization, World Scientific, Singapore, 1995, pp. 88-105
10. Hock, W., Schittkowski, K.: Test Examples for Nonlinear Programming Codes. Lect. Notes in Econ. Math. Syst. 187, Springer-Verlag, Berlin, 1981
11. Jiang, H.: Global convergence analysis of the generalized Newton and Gauss-Newton methods of the Fischer-Burmeister equation for the complementarity problem. Math. Oper. Res. 24, 529-543 (1999)
12. 1 equations. J. Oper. Res. Soc. Japan 29, 352-374 (1986)
13. Luo, Z.-Q., Mangasarian, O.L., Ren, J., Solodov, M.V.: New error bounds for the linear complementarity problem. Math. Oper. Res. 19, 880-892 (1994)
14. Pang, J.-S.: A posteriori error bounds for the linearly-constrained variational inequality problem. Math. Oper. Res. 12, 474-484 (1987)
15. Robinson, S.M.: Some continuity properties of polyhedral multifunctions. Math. Program. Study 14, 206-214 (1981)
16. Rockafellar, R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optimization 14, 877-898 (1976)
17. Stoer, J., Wechs, M., Mizuno, S.: High order infeasible-interior-point methods for sufficient linear complementarity problems. Math. Oper. Res. 23, 832-862 (1998)
18. Yamashita, N., Fukushima M.: Modified Newton methods for solving a semismooth reformulation of monotone complementarity problems. Math. Program. 76, 469-491 (1997)
19. Yamashita, N., Fukushima M.: The proximal point algorithm with genuine superlinear convergence for the monotone complementarity problem. SIAM J. Optim. 11, 364-379 (2001)