Restarting after Branching in the SDP Approach to MAX-CUT and Similar Combinatorial Optimization Problems

Journal of Combinatorial Optimization

Volumn 5, Issue 2, 2001, Pages 151-166

  Mitchell, John E ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Branch and cut; MAX CUT problems; Semidefinite programming

Indexed keywords

EID: 0006754305     PISSN: 13826905     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011416130639     Document Type: Article

References (19)

1. F. Alizadeh, "Interior point methods in semidefinite programming with applications to combinatorial optimization," SIAM Journal on Optimization, vol. 5, no. 1, pp. 13-51, 1995.
2. A. Ben-Tal and A. Nemirovskii, "Convex optimization in engineering: Modeling, analysis, algorithms," Technical Report, Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology, Technion-City, Haifa 32000, Israel, 1997.
3. S.J. Benson, Y. Ye, and X. Zhang, "Solving large-scale sparse semidefinite programs for combinatorial optimization," SIAM Journal on Optimization, vol. 10, no. 2, pp. 443-461, 2000.
4. S.J. Benson, Y. Ye, and X. Zhang, "Mixed linear and semidefinite programming for combinatorial and quadratic optimization," Optimization Methods and Software, vol. 11, pp. 515-544, 1999.
5. B. Borchers and J.E. Mitchell, "Using an interior point method in a branch and bound algorithm for integer programming," Technical Report 195, Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, 1991. Revised July 7, 1992.
6. A. de Silva and D. Abramson, "A parallel interior point method and its application to facility location problems," Computational Optimization and Applications, vol. 9, pp. 249-273, 1998.
7. M.X. Goemans, "Semidefinite programming in combinatorial optimization," Mathematical Programming, vol. 79, pp. 143-161, 1997.
8. M.X. Goemans and D.P. Williamson, "Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming," J. Assoc. Comput. Mach., vol. 42, pp. 1115-1145, 1995.
9. C. Helmberg, "Fixing variables in semidefinite relaxations," SIAM Journal on Matrix Analysis and Applications, vol. 21, no. 3, pp. 952-969, 2000.
10. C. Helmberg, S. Poljak, F. Rendl, and H. Wolkowicz, "Combining semidefinite and polyhedral relaxations for integer programs," in Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science, E. Balas and J. Clausen, (Eds.), volume 920, pages 124-134, Springer, 1995.
11. C. Helmberg and F. Rendl, "Solving quadratic (0,1)-problems by semidefinite programs and cutting planes," Mathematical Programming, vol. 82, pp. 291-315, 1998.
12. C. Helmberg, F. Rendl, R.J. Vanderbei, and H. Wolkowicz, "An interior point method for semidefinite programming," SIAM Journal on Optimization, vol. 6, pp. 342-361, 1996.
13. S. Joy, J.E. Mitchell, and B. Borchers, "Solving MAX-SAT and weighted MAX-SAT problems using branch-and-cut," Technical Report, Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180, 1998.
14. M. Kojima, S. Shindoh, and S. Hara, "Interior point methods for the monotone semidefinite linear complementarity problem in symmetric matrices," SIAM Journal on Optimization, vol. 7, pp. 86-125, 1997.
15. E.K. Lee and J.E. Mitchell, "Computational experience of an interior point SQP algorithm in a parallel branch-and-bound framework," in High Performance Optimization, II. Frenk et al., (Eds.), chapter 13, pp. 329-347, 2000.
16. Y.E. Nesterov and A.S. Nemirovsky, Interior Point Polynomial Methods in Convex Programming: Theory and Algorithms, SIAM Publications, SIAM: Philadelphia, USA, 1993.
17. Y.E. Nesterov and M.J. Todd, "Self-scaled barriers and interior-point methods for convex programming," Mathematics of Operations Research, vol. 22, pp. 1-42, 1997.
18. S. Poljak and F. Rendl, "Nonpolyhedral relaxations of graph-bisection problems," SIAM Journal on Optimization, vol. 5 pp. 467-487, 1995.
19. L. Vandenberghe and S. Boyd, "Semidefinite programming," SIAM Review, vol. 38, pp. 49-95, 1996.