A simply constrained optimization reformulation of KKT systems arising from variational inequalities

Applied Mathematics and Optimization

Volumn 40, Issue 1, 1999, Pages 19-37

  Facchinei, F ^a   Fischer, A ^b   Kanzow, C ^c   Peng, J M ^d  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b TU DORTMUND UNIVERSITY   (Germany)

^c UNIVERSITY OF HAMBURG   (Germany)

^d INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Constrained optimization; KKT conditions; Variational inequalities

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

KARUSH-KUHN-TUCKER SYSTEM; VARIATIONAL INEQUALITIES;

OPTIMIZATION;

EID: 0032649801     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900114     Document Type: Article

References (29)

1. Bertsekas DP (1982) Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York
2. Bonnans JF (1994) Local analysis of Newton type methods for variational inequalities and nonlinear programming. Appl Math Optim 29:161-186
3. Clarke FH (1983) Optimization and Nonsmooth Analysis. Wiley, New York
4. Cottle RW, Pang JS, Stone RE (1992) The Linear Complementarity Problem. Academic Press, Boston
5. Daniel JW (1973) Stability of the solution of definite quadratic programs. Math Programming 5:41-53
6. De Luca T, Facchinei F, Kanzow C (1996) A semismooth equation approach to the solution of nonlinear complementarity problems. Math Programming 75:407-439
7. Dennis JE, Schnabel RB (1983) Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood-Cliffs, NJ
8. Dirkse SP, Ferris MC (1995) MCPLIB: a collection of nonlinear mixed complementarity problems. Optim Methods Software 5:123-156
9. Facchinei F, Fischer A, Kanzow C (1997) A semismooth Newton method for variational inequalities: the case of box constraints. In Ferris MC, Pang JS (eds) Complementarity and Variational Problems: State of the Art. SIAM, Philadelphia, PA, pp 76-90
10. Facchinei F, Fischer A, Kanzow C (1998) Regularity properties of a semismooth reformulation of variational inequalities. SIAM J Optim 8:850-869
11. Facchinei F, Kanzow C (1997) A nonsmooth inexact Newton method for the solution of large-scale nonlinear complementarity problems. Math Programming 76:493-512
12. Facchinei F, Soares J (1997) A new merit function for nonlinear complementarity problems and a related algorithm. SIAM J Optim 7:225-247
13. Ferris MC, Pang JS (1997) Engineering and economic applications of complementarity problems. SIAM Rev 39:669-713
14. Fischer A (1992) A special Newton-type optimization method. Optim 24:269-284
15. Fischer A (1995) Solution of monotone complementarity problems with locally Lipschitzian functions. Math Programming 76:513-532
16. Fischer A (1998) A new constrained optimization reformulation for complementarity problems. J Optim Theory Appl 97:105-117
17. Fletcher R (1987) Practical Methods of Optimization, 2nd edn. Wiley, Chichester
18. Harker PT, Pang JS (1990) Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math Programming 48:161-220
19. Josephy NH (1979) Newton's method for generalized equations. Technical Summary Report 1965, Mathematics Research Center, University of Wisconsin, Madison, WI
20. Kanzow C, Kleinmichel H (1995) A class of Newton-type methods for equality and inequality constrained optimization. Optim Methods Software 5:173-198
21. Liu J (1995) Strong stability in variational inequalities. SIAM J Control Optim 33:725-749
22. Mifflin R (1977) Semismooth and semiconvex functions in constrained optimization. SIAM J Control Optim 15:957-972
23. Pang JS, Gabriel SA (1993) NE/SQP: a robust algorithm for the nonlinear complementarity problem. Math Programming 60:295-337
24. Pang JS, Qi L (1993) Nonsmooth equations: motivation and algorithms. SIAM J Optim 3:443-465
25. 1 minimization problems. J Optim Theory Appl 85:633-648
26. Peng JM (1995) A global method for monotone variational inequality problems with inequality constraints. Technical Report, State Key Laboratory of Scientific and Engineering Computing, Academic Sinica, Beijing, 1995
27. Qi L (1993) A convergence analysis of some algorithms for solving nonsmooth equations. Math Oper Res 18:227-244
28. Qi L, Sun J (1993) A nonsmooth version of Newton's method. Math Programming 58:353-368
29. Robinson SM (1980) Strongly regular generalized equations. Math Oper Res 5:43-62