New Constrained Optimization Reformulation of Complementarity Problems

Journal of Optimization Theory and Applications

Volumn 97, Issue 1, 1998, Pages 105-117

  Fischer, A ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Complementarity problems; Convex optimization; Reformulation as constrained minimization problems; Stationary points

Indexed keywords

CONSTRAINED OPTIMIZATION;

COMPLEMENTARITY PROBLEMS; CONSTRAINED MINIMIZATION PROBLEM; CONVEX OPTIMISATION; MINIMIZATION PROBLEMS; NONNEGATIVITY CONSTRAINTS; OPTIMIZATION REFORMULATION; REFORMULATION AS CONSTRAINED MINIMIZATION PROBLEM; REGULARITY CONDITION; STATIONARY POINTS; UNCONSTRAINED MINIMIZATION;

CONVEX OPTIMIZATION;

EID: 0032341736     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022627217515     Document Type: Article

References (35)

1. FACCHINEI, F., and SOARES, J., A New Merit Function for Nonlinear Complementarity Problems and a Related Algorithm, SIAM Journal on Optimization, Vol. 7, pp. 225-247, 1997.
2. FISCHER, A., A Newton-Type Method for Positive-Semidefinite Linear Complementarity Problems, Journal of Optimization Theory and Applications, Vol. 86, pp. 585-608, 1995.
3. FISCHER, A., An NCP-Function and Its Use for the Solution of Complementarity Problems, Recent Advances in Nonsmooth Optimization, Edited by D. Z. Du, L. Qi, and R. S. Womersley, World Scientific, Singapore, pp. 88-105, 1995.
4. FRIEDLANDER, A., MARTÍNEZ, J. M., and SANTOS, S. A., Solution of Linear Complementarity Problems Using Minimization with Simple Bounds, Journal of Global Optimization, Vol. 6, pp. 253-267, 1995.
5. FUKUSHIMA, M., Merit Functions for Variational Inequality and Complementarity Problems, Nonlinear Optimization and Applications, Edited by G. Di Pillo and F. Giannessi, Plenum Publishing Corporation, New York, New York, pp. 155-170, 1996.
6. GEIGER, C., and KANZOW, C., On the Resolution of Monotone Complementarity Problems, Computational Optimization and Applications, Vol. 5, pp. 155-173, 1996.
7. JIANG, H., and QI, L., A New Nonsmooth Equations Approach to Nonlinear Complementarities, SIAM Journal on Control and Optimization, Vol. 35, pp. 178-193, 1997.
8. KANZOW, C., Nonlinear Complementarity as Unconstrained Optimization, Journal of Optimization Theory and Applications, Vol. 88, pp. 139-155, 1996.
9. MONTEIRO, R. D. C., PANG, J. S., and WANG, T., A Positive Algorithm for the Nonlinear Complementarity Problem, SIAM Journal on Optimization, Vol. 5, pp. 129-148, 1995.
10. MORÉ, J. J., Global Methods for Nonlinear Complementarity Problems, Mathematics of Operations Research, Vol. 21, pp. 589-614, 1996.
11. PANG, J. S., and GABRIEL, S. A., NE/SQP: A Robust Algorithm for the Nonlinear Complementarity Problem, Mathematical Programming, Vol. 60, pp. 295-337, 1993.
12. PENG, J. M., and YUAN, Y. X., Unconstrained Methods for Generalized Complementarity Problems, Journal of Computational Mathematics, Vol. 15, pp. 253-264, 1997.
13. SUBRAMANIAN, P. K., Gauss-Newton Methods for the Complementarity Problem, Journal of Optimization Theory and Applications, Vol. 77, pp. 467-482, 1993.
14. TAJI, K., and FUKUSHIMA, M., Optimization-Based Globally Convergent Methods for the Nonlinear Complementarity Problem, Journal of the Operations Research Society of Japan, Vol. 37, pp. 310-331, 1994.
15. TSENG, P., YAMASHITA, N., and FUKUSHIMA, M., Equivalence of Complementarity Problems to Differentiable Minimization: A Unified Approach, SIAM Journal on Optimization, Vol. 6, pp. 446-460, 1996.
16. YAMASHITA, N., and FUKUSHIMA, M., On Stationary Points of the Implicit Lagrangian for Nonlinear Complementarity Problems, Journal of Optimization Theory and Applications, Vol. 84, pp. 653-663, 1995.
17. FISCHER, A., A Special Newton-Type Optimization Method, Optimization, Vol. 24, pp. 269-284, 1992.
18. MANGASARIAN, O. L., Equivalence of the Complementarity Problem to a System of Nonlinear Equations, SIAM Journal on Applied Mathematics, Vol. 31, pp. 89-92, 1976.
19. DE LUCA, T., FACCHINEI, F., and KANZOW, C., A Semismooth Equation Approach to the Solution of Nonlinear Complementarity Problems, Mathematical Programming, Vol. 75, pp. 407-439, 1997.
20. FISCHER, A., Solution of Monotone Complementarity Problems with Locally Lipschitzian Functions, Mathematical Programming, Vol. 76, pp. 513-532, 1997.
21. JIANG, H., Unconstrained Minimization Approaches to Nonlinear Complementarity Problems, Journal of Global Optimization, Vol. 9, pp. 169-181, 1996.
22. YAMASHITA, N., and FUKUSHIMA, M., Modified Newton Methods for Solving Semismooth Reformulations of Monotone Complementarity Problems, Mathematical Programming, Vol. 76, pp. 469-491, 1997.
23. FISCHER, A., On the Superlinear Convergence of a Newton-Type Method for LCP under Weak Conditions, Optimization Methods and Software, Vol. 6, pp. 83-107, 1995.
24. MANGASARIAN, O. L., and SOLODOV, M. V., Nonlinear Complementarity as Unconstrained and Constrained Minimization, Mathematical Programming, Vol. 62, pp. 277-297, 1993.
25. FERRIS, M. C., and RALPH, D., Projected Gradient Methods for Nonlinear Complementarity Problems via Normal Maps, Recent Advances in Nonsmooth Optimization, Edited by D. Z. Du, L. Qi, and R. S. Womersley, World Scientific, Singapore, pp. 57-87, 1995.
26. COTTLE, R. W., PANG, J. S., and STONE, R. E., The Linear Complementarity Problem, Academic Press, New York, New York, 1992.
27. KANZOW, C., YAMASHITA, N., and FUKUSHIMA, M., New NCP-Functions and Their Properties, Technical Report 104, Institute of Applied Mathematics, University of Hamburg, Hamburg, Germany, 1996.
28. CLARKE, F. H., Optimization and Nonsmooth Analysis, John Wiley and Sons, New York, New York, 1983.
29. JIANG, H., and QI, L., Local Uniqueness and Convergence of Iterative Methods for Nonsmooth Variational Inequalities, Journal of Mathematical Analysis and Applications, Vol. 196, pp. 314-331, 1995.
30. KANZOW, C., An Unconstrained Optimization Technique for Large-Scale Linearly Constrained Convex Minimization Problems, Computing, Vol. 53, pp. 101-117, 1994.
31. CONN, A. R., GOULD, N. I. M., and TOINT, P. L., Global Convergence of a Class of Trust-Region Algorithms for Optimization Problems with Simple Bounds, SIAM Journal on Numerical Analysis, Vol. 25, pp. 433-460, 1988.
32. FACCHINEI, F., and LUCIDI, S., A Class of Methods for Optimization Problems with Simple Bounds, Technical Report 336, IASI-CNR, Rome, Italy, 1992 (Revised 1995).
33. FRIEDLANDER, A., MARTÍNEZ, J. M., and SANTOS, S. A., A New Trust Region Algorithm for Bound Constrained Minimization, Applied Mathematics and Optimization, Vol. 30, pp. 235-266, 1994.
34. 1-Optimization Problems, Mathematical Programming, Vol. 64, pp. 277-294, 1994.
35. SOARES, J., JÚDICE, J., and FACCHINEI, F., An Active Set Newton Algorithm for Large-Scale Nonlinear Programs with Box Constraints, SIAM Journal on Optimization, Vol. 8, pp. 158-186, 1998.