Penalty function approach to linear trilevel programming

Journal of Optimization Theory and Applications

Volumn 93, Issue 1, 1997, Pages 183-197

  White, D J ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Penalty functions; Trilevel programming

Indexed keywords

ALGORITHM FOR SOLVING; CONSTRAINT SET; DECISION MAKERS; OBJECTIVE FUNCTIONS; PENALTY FUNCTION; PENALTY FUNCTION APPROACH; QUALITATIVE ADVANTAGES; STEP ALGORITHMS; TRILEVEL DECISION MAKINGS; TRILEVEL PROGRAMMING;

DECISION MAKING;

EID: 0031519352     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022610103712     Document Type: Article

References (13)

1. BARD, J. F., An Investigation of the Linear Three-Level Programming Problem, IEEE Transactions on Systems, Man, and Cybernetics, Vol. 14, pp. 711-717, 1984.
2. WEN, U. P., and HSU, S. T., Linear Bilevel Programming Problems: A Review, Journal of the Operational Research Society, Vol. 42, pp. 125-134, 1991.
3. VINCENTE, L. N., and CALAMAI, P., Bilevel and Multilevel Programming: A Bibliography Review, Journal of Global Optimization, Vol. 5, pp. 291-306, 1994.
4. WEN, U. P., and BIALAS, W., The Hybrid Algorithm for Solving the Three-Level Programming Problem, Computers and Operations Research, Vol. 13, pp. 367-377, 1986.
5. BENSON, H. P., On the Structure and Properties of a Linear Multilevel Programming Problem, Journal of Optimization Theory and Applications, Vol. 9, pp. 353-373, 1989.
6. BARD, J., and FALK, J., An Explicit Solution to the Multilevel Programming Problem, Computers and Operations Research, Vol. 9, pp. 77-100, 1982.
7. CASSIDY, R. G., KIRBY, M. J. L., and RAIKE, W. M., Efficient Distribution of Resources through Three Levels of Government, Management Science, Vol. 17B, pp. 462-473, 1971.
8. WEN, U. P., Mathematical Methods for Multilevel Linear Programming, PhD Dissertation, Department of Industrial Engineering, State University of New York at Buffalo, 1981.
9. ZANGWILL, W. I., Nonlinear Programming: A Unified Approach, Prentice Hall, Englewood Cliffs, New Jersey, 1969.
10. WHITE, D. J., and ANANDALINGAM, G., A Penalty Function Approach for Solving Bilevel Linear Programs, Journal of Global Optimization, Vol. 3, pp. 397-419, 1993.
11. TUY, H., Concave Programming under Linear Constraints, Soviet Mathematics, Vol. 5, pp. 1437-1440, 1964.
12. SHERALI, H. D., and SHETTY, C. M., A Finitely Convergent Algorithm for Bilinear Programming Problems Using Polar Cuts and Disjunctive Face Cuts, Mathematical Programming, Vol. 12, pp. 14-31, 1980.
13. KONNO, H., A Cutting-Plane Algorithm for Solving Bilinear Programs, Mathematical Programming, Vol. 11, pp. 14-27, 1976.