Mean value cross decomposition applied to integer programming problems

European Journal of Operational Research

Volumn 97, Issue 1, 1997, Pages 124-138

  Holmberg, Kaj ^a  

^a LINKÖPING INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Decomposition methods; Integer programming; Lagrange multipliers; Mathematical programming

Indexed keywords

COMPUTATIONAL METHODS; LAGRANGE MULTIPLIERS; LINEAR PROGRAMMING; PROBLEM SOLVING;

DECOMPOSITION METHODS; OPTIMAL OBJECTIVE FUNCTION VALUE;

INTEGER PROGRAMMING;

EID: 0031075080     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(96)00139-7     Document Type: Article

References (16)

1. Benders, J.F. (1962), "Partitioning procedures for solving mixed-variables programming problems", Numerische Mathematik 4, 238-252.
2. Dantzig, G.B., and Wolfe, P. (1960), "Decomposition principle for linear programs", Operations Research 8, 101-111.
3. Brown, G.W. (1949), "Some notes on computation of games solutions", RAND Report P-78, The RAND Corporation, Santa Monica, CA.
4. Geoffrion, A.M. (1974), "Lagrangean relaxation for Integer Programming", Mathematical Programming Study 2, 82-114.
5. Held, M., Wolfe, P., and Crowder, H.P. (1974), "Validation of subgradient optimization", Mathematical Programming 6, 62-88.
6. Holmberg, K. (1990), "On the convergence of cross decomposition", Mathematical Programming 47, 269-296.
7. Holmberg, K. (1992), "Linear mean value cross decomposition: A generalization of the Kornai-Liptak method", European Journal of Operational Research 62, 55-73.
8. Holmberg, K. (1994a), "A convergence proof for linear mean value cross decomposition", Zeitschrift für Operations Research 39, 157-186.
9. Holmberg, K. (1994b), "Cross decomposition applied to Integer Programming problems: Duality gaps and convexification in parts", Operations Research 42, 657-668.
10. Kornai, J., and Liptak, Th. (1965), "Two-level planning", Econometrica 33, 141-169.
11. Minoux, M. (1986), Mathematical Programming: Theory and Algorithms, Wiley, Chichester.
12. Mulvey, J.M., and Crowder, H.P. (1979), "Cluster analysis: An application of Lagrangian relaxation", Management Science 25, 329-340.
13. Poljak, B.T. (1967), "A general method of solving extremum problems", Soviet Mathematics Doklady 8, 593-597.
14. Poljak, B.T. (1969), "Minimization of unsmooth functionals", USSR Computational Mathematics and Mathematical Physics 9, 14-29.
15. Robinson, J. (1951), "An iterative method of solving a game", Annals of Mathematics 54, 296-301.
16. Van Roy, T.J. (1983), "Cross decomposition for mixed integer programming", Mathematical Programming 25, 46-63.