A nonlinear approach to a class of combinatorial optimization problems

Statistica Neerlandica

Volumn 52, Issue 2, 1998, Pages 162-184

  Warners, J P ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Frequency assignment; Gradient descent; Interior point methods; Nonlinear optimization

Indexed keywords

EID: 0032370716     PISSN: 00390402     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9574.00076     Document Type: Article

References (20)

1. BAZARAA, M. S., H. D. SHERALI and C. M. SHETTY (1993), Nonlinear programming: theory and algorithms, John Wiley and Sons, New York.
2. BENTHEM, H. P. VAN (1995), GRAPH: Generating radio link frequency assignment problems heuristically, Master's thesis, Faculty of Technical Mathematics and Informatics, Delft University of Technology, The Netherlands.
3. CHVÁTAL, V., Edmonds polytopes and a hierarchy of combinatorial problems, Discrete Mathematics 4, 305-337.
4. DIKIN, I. I. (1967), Iterative solution of problems of linear and quadratic programming, Doklady Akademiia Nauk SSSR 174, 747-748. Translated into English in Soviet Mathematics Doklady 8, 674-675.
5. DIKIN, I. I. (1967), Iterative solution of problems of linear and quadratic programming, Doklady Akademiia Nauk SSSR 174, 747-748. Translated into English in Soviet Mathematics Doklady 8, 674-675.
6. Gu, J. (1994), Global optimization for satisfiability (SAT) problem, IEEE Transactions on Knowledge and Data Engineering 6, 361-381.
7. KAMATH, A. P., N. K. KARMARKAR, K. G. RAMAKRISHNAN and M. G. C. RESENDE (1990), Computational experience with an interior point algorithm on the satisfiability problem, Annals of Operations Research 25, 43-58.
8. KARMARKAR, N. (1984), A new polynomial-time algorithm for linear programming, Combinatorica 4, 373-395.
9. KARMARKAR, N. (1990), An interior-point approach to NP-complete problems - part I, Contemporary Mathematics 114, 297-308.
10. KARMARKAR, N., M. G. C. RESENDE and K. G. RAMAKRISHNAN (1991), An interior point algorithm to solve computationally difficult set covering problems, Mathematical Programming 52, 597-618.
11. LOVÁSZ, L. and A. SCHRIJVER (1991), Cones of matrices and set-functions and 0-1 optimization, SIAM Journal on Optimization 1, 166-190.
12. SCHRIJVER, A. (1986), Theory of linear and integer programming, John Wiley & Sons, New York.
13. SHERALI, H. D. and W. P. ADAMS (1990), A hierarchy of relaxations between the continuous and convex hull representations for 0-1 programming problems, SIAM Journal on Discrete Mathematics 3, 411-430.
14. SHOR, N. Z. (1990), Dual quadratic estimates in polynomial and boolean programming, Annals of Operations Research 25, 163-168.
15. SÖRENSEN, D. C. (1982), Newton's method with a model trust region modification, SIAM Journal on Numerical Analysis 19, 409-426.
16. TIOURINE, S., C. HURKENS and J. K. LENSTRA (1995), An overview of algorithmic approaches to frequency assignment problems, Technical report, CALMA project, Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands.
17. WARNERS, J. P. (1995), A potential reduction approach to the radio link frequency assignment problem, Master's thesis, Faculty of Technical Mathematics and Informatics, Delft University of Technology, The Netherlands.
18. WARNERS, J. P., T. TERLAKY, C. ROOs and B. JANSEN (1997a), Potential reduction algorithms for structured combinatorial optimization problems, Operations Research Letters 21, 55-64.
19. WARNERS, J. P., T. TERLAKY, C. ROOs and B. JANSEN (1997b), A potential reduction approach to the frequency assignment problem, Discrete Applied Mathematics 78, 251-282.
20. ZHANG, Y. (1996), Solving large-scale linear programs by interior point methods under the MAT-LAB environment, Technical Report TR96-01, Department of Mathematics and Statistics, University of Baltimore County, Baltimore, Maryland 21222-5398.