Enumeration Approach for Linear Complementarity Problems Based on a Reformulation-Linearization Technique

Journal of Optimization Theory and Applications

Volumn 99, Issue 2, 1998, Pages 481-507

  Sherali, H D ^a   Krishnamurthy, R S ^b   Al Khayyal, F A ^c  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b Research Group   (United States)

^c Georgia Institute of Technology   (United States)

Author keywords

Bilinear programming; Implicit enumeration; Lagrangian relaxation; Linear complementarity problem; Reformulation linearization technique

Indexed keywords

GLOBAL OPTIMIZATION; INTEGER PROGRAMMING; LAGRANGE MULTIPLIERS;

BILINEAR PROGRAMMING; ENUMERATION APPROACHES; GLOBAL OPTIMIZATION ALGORITHM; IMPLICIT ENUMERATION; LAGRANGIAN RELAXATIONS; LINEAR COMPLEMENTARITY PROBLEMS; MATRIX; PROBLEM-BASED; REFORMULATION-LINEARIZATION TECHNIQUE; SPECIAL STRUCTURE;

LINEARIZATION;

EID: 0032336172     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021734613201     Document Type: Article

References (29)

1. MURTY, K. G., Linear Complementarity, Linear and Nonlinear Programming, Helderman Verlag, Berlin, Germany, 1988.
2. COTTLE, R. W., PANG, J. S., and STONE, R. E., The Linear Complementarity Problem, Academic Press, San Diego, California, 1992.
3. YE, Y., and PARDALOS, P. M., A Class of Linear Complementarity Problems Solvable in Polynomial Time, Linear Algebra and Its Applications, Vol. 152, pp. 3-17, 1991.
4. KOJIMA, M., MEGIDDO, N., NOMA, T., and YOSHISE, A., A Unified Approach to Interior-Point Algorithms for Linear Complementarity Problems, Lecture Notes in Computer Science, Springer Verlag, Berlin, Germany, Vol. 538, 1991.
5. PARDALOS, P. M., YE, Y., HAN, C. G., and KALINSKI, J., Solution of P-Matrix Linear Complementarity Problems Using a Potential Reduction Algorithm, SIAM Journal on Matrix Analysis and Applications, Vol. 14, pp. 1048-1060, 1993.
6. AL-KHAYYAL, F. A., An Implicit Enumeration Procedure for the Linear Complementarity Problem, Mathematical Programming Study, Vol. 17, pp. 1-21, 1987.
7. PARDALOS, P. M., and ROSEN, J. B., Global Optimization Approach to the Linear Complementarity Problem, SIAM Journal on Scientific and Statistical Computations, Vol. 9, pp. 341-353, 1988.
8. JUDICE, J. J., and FAUSTINO, A. M., An Experimental Investigation of Enumeration Methods for Linear Complementarity Problems, Computers and Operations Research, Vol. 15, pp. 417-426, 1988.
9. MANGASARIAN, O., The Linear Complementarity Problem as a Separable Bilinear Program, Journal of Global Optimization, Vol. 6, pp. 153-161, 1995.
10. SHERALI, H. D., KRISHNAMURTHY, R., and AL-KHAYYAL, F. A., Enhanced Intersection Cutting Plane Approach for Linear Complementarity Problems, Journal of Optimization Theory Applications, Vol. 90, pp. 183-201, 1996.
11. DORN, W. S., Self-Dual Quadratic Programs, SIAM Journal on Applied Mathematics, Vol. 9, pp. 51-54, 1961.
12. EAVES, B. C., The Linear Complementarity Problem, Management Science, Vol. 17, pp. 612-634, 1971.
13. MANGASARIAN, O., Equivalence of the Complementarity Problem to a System of Nonlinear Equations, SIAM Journal on Applied Mathematics, Vol. 31, pp. 89-92, 1977.
14. AL-KHAYYAL, F. A., On Solving Linear Complementarity Problems as Bilinear Programs, Arabian Journal for Science and Engineering, Vol. 15, pp. 639-646, 1990.
15. SHERALI, H. D., and ADAMS, W. P., A Hierarchy of Relaxations between the Continuous and Convex Hull Representations for Zero-One Programming Problems, SIAM Journal on Discrete Mathematics, Vol. 3, pp. 411-430, 1990.
16. SHERALI, H. D., and ADAMS, W. P., A Hierarchy of Relaxations and Convex Hull Characterizations for Mixed-Integer Zero-One Programming Problems, Discrete Applied Mathematics, Vol. 52, pp. 83-106, 1994.
17. ADAMS, W. P., and SHERALI, H. D., Mixed-Integer Bilinear Programming Problems, Mathematical Programming, Vol. 59, pp. 279-305, 1993.
18. SHERALI, H. D., and MYERS, D. C., The Design of Branch-and-Bound Algorithms for a Class of Nonlinear Integer Programs, Annals of Operations Research, Vol. 5, pp. 463-484, 1986.
19. SHERALI, H. D., and ULULAR, O., A Primal-Dual Conjugate Subgradient Algorithm for Specially Structured Linear and Convex Programming Problems, Applied Mathematics and Optimization, Vol. 20, pp. 193-221, 1989.
20. BAZARAA, M. S., SHERALI, H. D., and SHETTY, C. M., Nonlinear Programming: Theory and Algorithms, 2nd Edition, John Wiley and Sons, New York, New York, 1993.
21. CAMERINI, P. M., FRATTA, L., and MAFFIOLI, F., On Improving Relaxation Methods by Modified Gradient Techniques, Mathematical Programming Study, Vol. 3, pp. 26-34, 1975.
22. SHERALI, H. D., and CHOI, G., Recovery of Primal Solutions When Using Subgradient Optimization Methods to Solve Lagrangian Duals of Linear Programs, Operations Research Letters, Vol. 19, pp. 105-113, 1996.
23. SHOR, N. S., Minimization Methods for Nondifferentiable Functions, Springer Verlag, Berlin, Germany, 1985 (Translated from Russian).
24. RARDIN, R., and UNGER, V., Surrogate Constraints and the Strength of Bounds Derived from 0-1 Benders Partitioning Procedures, Operations Research, Vol. 24, pp. 1169-1175, 1976.
25. PARDALOS, P. M., and ROSEN, J. B., Bounds for Solution Sets of Linear Complementarity Problems, Discrete Applied Mathematics, Vol. 17, pp. 255-261, 1987.
26. L'ECUYER, P., and COTE, S., Implementing a Random Number Package with Splitting Facilities, ACM Transactions on Mathematical Software, Vol. 17, pp. 98-111, 1991.
27. LIN, Y. Y., and PANG, J. S., Iterative Methods for Large Convex Quadratic Programs, SIAM Journal on Control and Optimization, Vol. 25, pp. 383-411, 1987.
28. MARSTEN, R. E., The Design of the XMP Linear Programming Library, ACM Transactions of Mathematical Software, Vol. 7, pp. 481-497, 1981.
29. RAMARAO, B., and SHETTY, C. M., Application of Disjunctive Programming to the Linear Complementarity Problem, Naval Research Logistics Quarterly, Vol. 31, pp. 589-600, 1984.