A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems

Mathematical Programming, Series B

Volumn 76, Issue 3, 1997, Pages 493-512

  Facchinei, Francisco ^a   Kanzow, Christian ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF HAMBURG   (Germany)

Author keywords

Inexact Newton methods; Large scale problems; Nonlinear complementarity problems; Nonsmooth equations

Indexed keywords

EID: 0001151466     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02614395     Document Type: Article

References (36)

1. D.P. Bertsekas, Constrained Optimization and Lagrange Multiplier Methods (Academic, New York, NY, 1982).
2. C. Chen and O.L. Mangasarian, A class of smoothing functions for nonlinear and mixed complementarity problems, Computational Optimization and Applications 5 (1996) 97-138.
3. F.H. Clarke, Optimization and Nonsmooth Analysis (Wiley, New York, NY, 1983).
4. R.W. Cottle, J.-S. Pang and R.W. Stone, The Linear Complementarity Problem (Academic, New York, NY, 1992).
5. T. De Luca, F. Facchinei and C. Kanzow, A semismooth equation approach to the solution of nonlinear complementarity problems, Mathematical Programming 75 (1996) 407-439
6. R.S. Dembo, S.C. Eisenstat and T. Steihaug, Inexact Newton methods, SIAM Journal on Numerical Analysis 19 (1982) 400-408.
7. J.E. Dennis and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, NJ, 1983).
8. S.P. Dirkse and M.C. Ferris, MCPLIB: A collection of nonlinear mixed complementarity problems, Optimization Methods and Software 5 (1995) 319-345.
9. 1 functions and the Maratos effect, Operations Research Letters 17 (1995) 131-137.
10. F. Facchinei and J. Soares, A new merit function for nonlinear complementarity problems and a related algorithm, SIAM Journal on Optimization 7 (1997) 225-247.
11. M.C. Ferris and J.-S. Pang, Engineering and economic applications of complementarity problems, Technical Report 95-07, Computer Sciences Department, University of Wisconsin (Madison, WI, 1995).
12. A. Fischer, A special Newton-type optimization method, Optimization 24 (1992) 269-284.
13. A. Fischer, An NCP-function and its use for the solution of complementarity problems, in: D.-Z. Du, L. Qi and R. Womersley, eds., Recent Advances in Nonsmooth Optimization (World Scientific, Singapore, 1995) 88-105.
14. A. Fischer, Solution of monotone complementarity problems with locally Lipschitzian functions, Preprint 9/1995, Institute of Numerical Mathematics, Technical University of Dresden (Dresden, 1995).
15. S.A. Gabriel and J.-S. Pang, An inexact NE/SQP method for solving the nonlinear complementarity problem, Computational Optimization and Applications 1 (1992) 67-91.
16. L. Grippo, F. Lampariello and S. Lucidi, A nonmonotone line search technique for Newton's method, SIAM Journal on Numerical Analysis 23 (1986) 707-716.
17. M.A. Gomes-Ruggiero, J.M. Martínez and S.A. Santos, Solving nonsmooth equations by means of quasi-Newton methods with globalization, in: D.-Z. Du, L. Qi and R. Womersley, eds., Recent Advances in Nonsmooth Optimization (World Scientific, Singapore, 1995) 121-140.
18. P.T. Harker and J.-S. Pang, Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications, Mathematical Programming 48 (1990) 161-220.
19. P.T. Harker and B. Xiao, Newton's method for the nonlinear complementarity problem: A B-differentiable equation approach, Mathematical Programming 48 (1990) 339-357.
20. G. Isac, Complementarity Problems, Lecture Notes in Mathematics, Vol. 1528 (Springer, Berlin, 1992).
21. H. Jiang and L. Qi, A new nonsmooth equations approach to nonlinear complementarity problems, SIAM Journal on Control and Optimization 35 (1997) 178-193.
22. L. Lukšan, Inexact trust region method for large sparse systems of nonlinear equations, Journal of Optimization Theory and Applications 81 (1994) 569-590.
23. O.L. Mangasarian, Equivalence of the complementarity problem to a system of nonlinear equations, SIAM Journal on Applied Mathematics 31 (1976) 89-92.
24. J.M. Martínez and L. Qi, Inexact Newton methods for solving nonsmooth equations, Journal of Computational and Applied Mathematics 60 (1995) 127-145.
25. R. Mifflin, Semismooth and semiconvex functions in constrained optimization, SIAM Journal on Control and Optimization 15 (1977) 957-972.
26. J.J. Moré and D.C. Sorensen, Computing a trust region step, SIAM Journal on Scientific and Statistical Computing 4 (1983) 553-572.
27. J.-S. Pang, Inexact Newton methods for the nonlinear complementarity problem. Mathematical Programming 36 (1986) 54-71.
28. J.-S. Pang, Complementarity problems, in: R. Horst and P.M. Pardalos, eds., Handbook of Global Optimization (Kluwer Academic, Dordrecht, 1994) 271-338.
29. J.-S. Pang and S.A. Gabriel, NE/SQP: A robust algorithm for the nonlinear complementarity problem, Mathematical Programming 60 (1993) 295-337.
30. J.-S. Pang and L. Qi, Nonsmooth equations: Motivation and algorithms, SIAM Journal on Optimization 3 (1993) 443-465.
31. B.N. Pshenichny and J.M Danilin, Numerical Methods in Extremal Problems (Mir, Moscow, 1978).
32. L. Qi, A convergence analysis of some algorithms for solving nonsmooth equations, Mathematics of Operations Research 18 (1993) 227-244.
33. L. Qi and J. Sun, A nonsmooth version of Newton's method, Mathematical Programming 58 (1993) 353-368.
34. S.M. Robinson, Generalized equations, in: A. Bachem, M. Groetschel and B. Korte, eds., Mathematical Programming: The State of the Art (Springer, Berlin, 1983) 346-367.
35. P.K. Subramanian, Gauss-Newton methods for the complementarity problem. Journal of Optimization Theory and Applications 77 (1993) 467-482.
36. Ph.L. Toint, A non-monotone trust-region algorithm for nonlinear optimization subject to convex constraints, Report 92/94, Department of Mathematics, FUNDP (Namur, 1994).