Bregman proximal relaxation of large-scale 0-1 problems

Computational Optimization and Applications

Volumn 15, Issue 1, 2000, Pages 33-44

  Kiwiel, Krzysztof C ^a   Lindberg, P O ^b   Nõu, Andreas ^c  

^a SYSTEMS RESEARCH INSTITUTE   (Poland)

^b LINKÖPING UNIVERSITY   (Sweden)

^c ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; HEURISTIC METHODS; PROBLEM SOLVING; RANDOM PROCESSES; SET THEORY;

BREGMAN PROXIMAL METHOD; CONVEX PROGRAMMING; LAGRANGIAN RELAXATION;

LINEAR PROGRAMMING;

EID: 0033640511     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008770914218     Document Type: Article

References (35)

1. E. Balas and M.C. Carrera, "A dynamic subgradient-based branch-and-bound procedure for set covering," Operations Research, vol. 44, pp. 875-890, 1996.
2. E. Balas and A. Ho, "Set covering algorithms using cutting planes, heuristics and subgradient optimization: A computational study," Mathematical Programming Study, vol. 12, pp. 37-60, 1980.
3. H.H. Bauschke and J.M. Borwein, "Legendre functions and the method of random Bregman projections," Journal of Convex Analysis, vol. 4, pp. 27-67, 1997.
4. J.E. Beasley, "An algorithm for set covering problems," European Journal of Operations Research, vol. 31, pp. 85-93, 1987.
5. J.E. Beasley, "A Lagrangian heuristic for set covering problems," Naval Research Logistics Quarterly, vol. 37, pp. 151-164, 1990.
6. J.E. Beasley and K. Jörnsten, "Enhancing an algorithm for set covering problems," European Journal of Operations Research, vol. 58, pp. 293-300, 1992.
7. D.P. Bertsekas, Nonlinear Programming, Athena Scientific: Belmont, MA, 1995.
8. G.R. Bitran and A.C. Hax, "Disaggregation and resource allocation using convex knapsack problems with bounded variables," Management Science, vol. 27, pp. 431-441, 1981.
9. R.S. Burachik, A.N. Iusem, and B.F. Svaiter, "Enlargement of monotone operators with applications to variational inequalities," Set-Valued Analysis, vol. 5, pp. 159-180, 1997.
10. A. Caprara, M. Fischetti, and P. Toth, "A heuristic algorithm for the set covering problem," in Integer Programming and Combinatorial Optimization, W.H. Cunningham, S.T. McCormick, and M. Queyranne (Eds.), Lecture Notes in Computer Science 1084, Springer-Verlag: Berlin, 1996, pp. 72-84.
11. Y. Censor and S.A. Zenios, "Proximal minimization algorithm with D-functions," Journal of Optimization Theory and Applications, vol. 73, pp. 451-464, 1992.
12. S. Ceria, P. Nobili, and A. Sassano, "A Lagrangian-based heuristic for large-scale set covering problems," Mathematical Programming, vol. 81, pp. 215-228, 1998.
13. G. Chen and M. Teboulle, "Convergence analysis of a proximal-like minimization algorithm using Bregman functions," SIAM Journal on Optimization, vol. 3, pp. 538-543, 1993.
14. J. Eckstein, "Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming," Mathematics of Operations Research, vol. 18, pp. 202-226, 1993.
15. J. Eckstein, "Approximate iterations in Bregman-function-based proximal algorithms," Mathematical Programming, vol. 83, pp. 113-123, 1998.
16. J. Eckstein and M.C. Ferris, "Smooth methods of multipliers for complementarity problems," Research Report RRR 27-96, RUTCOR, Rutgers Univ., New Brunswick, NJ 08903, August 1996, revised February 1997.
17. T.A. Feo and M.G.C. Resende, "A probabilistic heuristic for a computationally difficult set covering problems," Operations Research Letters, vol. 8, pp. 67-71, 1989.
18. M.L. Fisher and P. Kedia, "Optimal solutions of set covering/partitioning problems using dual heuristics," Management Science, vol. 36, pp. 674-688, 1990.
19. S. Haddadi, "Simple Lagrangian heuristic for the set covering problem," European Journal of Operations Research, vol. 97, pp. 200-204, 1997.
20. J.-B. Hiriart-Urruty and C. Lemaréchal, Convex Analysis and Minimization Algorithms, Springer-Verlag: Berlin, 1993.
21. A.N. Iusem, "Some properties of generalized proximal point methods for quadratic and linear programming," Journal of Optimization Theory and Applications, vol. 85, pp. 593-612, 1995.
22. A.N. Iusem, B.F. Svaiter, and J.X. da Cruz Neto, "Central paths, generalized proximal point methods and Cauchy trajectories in Riemannian manifolds," Technical report, IMPA, Rio de Janeiro, Brasil, 1996. SIAM Journal on Control and Optimization, vol. 37, pp. 566-588, 1999.
23. K.C. Kiwiel, "Free-steering relaxation methods for problems with strictly convex costs and linear constraints," Mathematics of Operations Research, vol. 22, pp. 326-349, 1997a.
24. K.C. Kiwiel, "Proximal minimization methods with generalized Bregman functions," SIAM Journal on Control and Optimization, vol. 35, pp. 1142-1168, 1997b.
25. K.C. Kiwiel, "A bundle Bregman proximal method for convex nondifferentiable minimization," Mathematical Programming, vol. 85, pp. 241-258, 1999.
26. P.O. Lindberg and A. Nõu, "A combined probabilistic and differentiable dual approach to large-scale binary optimization problems," Technical Report TRITA/MAT-97-OS13, Department of Mathematics, Royal Institute of Technology, Stockholm, 1997.
27. L.A.N. Lorena and F.B. Lopes, "A surrogate heuristic for set covering problems," European Journal of Operations Research, vol. 79, pp. 138-150, 1994.
28. S.S. Nielsen and S.A. Zenios, "A massively parallel algorithm for nonlinear stochastic network problems," Operations Research, vol. 41, pp. 319-337, 1993a.
29. S.S. Nielsen and S.A. Zenios, "On the massively parallel solution of linear network flow problems," DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 12, pp. 349-369, 1993b.
30. S.S. Nielsen and S.A. Zenios, "Proximal minimizations with D-functions and the massively parallel solution of linear network programs," Computational Optimization and Applications, vol. 1, pp. 375-398, 1993c.
31. S.S. Nielsen and S.A. Zenios, "Massively parallel proximal algorithms for solving linear stochastic network programs," International Journal on Supercomputer Applications, vol. 7, pp. 349-364, 1994.
32. R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
33. P. Tseng, "Dual ascent methods for problems with strictly convex costs and linear constraints: A unified approach," SIAM Journal on Control and Optimization, vol. 28, pp. 214-242, 1990.
34. D. Wedelin, "An algorithm for large scale 0-1 integer programming with application to airline crew scheduling," Annals of Operations Research, vol. 57, pp. 283-301, 1995a.
35. D. Wedelin, "The design of a 0-1 integer optimizer and its application in the Carmen system," European Journal of Operations Research, vol. 87, pp. 722-730, 1995b.