×
Van Roy, Tony J.

Cross decomposition for mixed integer programming. (English) Zbl 0505.90057

Math. Program. 25, 46-63 (1983).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0505.90057

Cited in 2 Reviews
Cited in 51 Documents

MSC:

90C11 Mixed integer programming
65K05 Numerical mathematical programming methods
90C06 Large-scale problems in mathematical programming

Keywords:

duality gap; Lagrangean relaxation; Benders decomposition; cross- decomposition; capacitated facility location problem; Lagrangean multipliers; mixed integer linear programs; primal and dual substructure
Cite Review PDF
Full Text: DOI

References:

[1] E. Balas and C. Bergthaller, ”Benders method revisited”, Management Sciences Report 401, Carnegie-Mellon University (Pittsburgh, PA, 1977). · Zbl 0512.65049
[2] J.F. Benders, ”Partitioning for solving mixed variables programming problems’,Numerische Mathematik 4 (1962), 238–252. · Zbl 0109.38302 · doi:10.1007/BF01386316
[3] G.B. Dantzig and P. Wolfe, ”Decomposition principle for linear programs”,Operations Research 8 (1960) 101–111. · Zbl 0093.32806 · doi:10.1287/opre.8.1.101
[4] M.L. Fisher, W.D. Northup and J.F. Shapiro, ”Using duality to solve discrete optimizations problems: Theory and computational experience”,Mathematical Programming Study 3 (1975) 56–94. · Zbl 0367.90087
[5] M.L. Fisher, ”The Lagrangean relaxation method for solving integer programming problems”,Management Science 27 (1981) 1–18. · Zbl 0466.90054 · doi:10.1287/mnsc.27.1.1
[6] A.M. Geoffrion, ”Lagrangean relaxation for integer programming”.Mathematical Programming Study 2 (1974) 82–113. · Zbl 0395.90056
[7] G.W. Graves and T.J. Van Roy, ”Decomposition for large scale linear and mixed integer linear programming”, Working Paper, Graduate School of Management. UCLA (Los Angeles, November 1979).
[8] L.S. Lasdon,Optimization theory for large systems (MacMillan, New York, 1970). · Zbl 0224.90038
[9] D. McDaniel and M. Devine, ”A modified Benders’ partitioning algorithm for mixed integer programming”,Management Science (1977) 312–379. · Zbl 0371.90102
[10] D.J. Sweeney and R.A. Murphy, ”A method of decomposition for integer programs”,Operations Research 27 (1979) 1128–1141. · Zbl 0442.90063 · doi:10.1287/opre.27.6.1128
[11] T.J. Van Roy, ”A cross decomposition algorithm for capacitated facility location”, to appear inOperations Research. · Zbl 0594.90022
[12] T.J. Van Roy, ”Cross decomposition for large-scale mixed integer linear programming with applications to facility location on distribution networks”, doctoral dissertation, Applied Sciences, Katholieke Universiteit Leuven (1980).
[13] L.A. Wolsey, ”A resource decomposition algorithm for general mathematical programs”,Mathematical Programming Study 14 (1981) 244–257. · Zbl 0449.90085
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.