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Dyer, M. E.

Calculating surrogate constraints. (English) Zbl 0464.90067

Math. Program. 19, 255-278 (1980).
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Cited in 37 Documents

MSC:

90C30 Nonlinear programming
49M29 Numerical methods involving duality
49M37 Numerical methods based on nonlinear programming
90C10 Integer programming
90C25 Convex programming
65K05 Numerical mathematical programming methods

Keywords:

surrogate constraints; subgradient methods; generalised programming; surrogate duality; convergence; Lagrangean methods; algorithm
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\textit{M. E. Dyer}, Math. Program. 19, 255--278 (1980; Zbl 0464.90067)
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References:

[1] K. Banerjee, ”Generalized Lagrange multipliers in dynamic programming”, Research report ORC 71-12, Operations Research Center, University of California, Berkeley, CA (1971).
[2] S. Bolwell and M.H. Karwan, ”Efficient use of surrogate duality in 0–1 integer programming”, Industrial Engineering report, State University of New York at Buffalo, NY (1979).
[3] S. Bolwell and M.H. Karwan, ”A hybrid surrogate dual-cutting plane approach to integer programming”, Industrial Engineering report, State University of New York at Buffalo, NY (1979).
[4] G.H. Bradley, ”Transformation of integer programs to knapsack problems”,Discrete Mathematics 1 (1971) 29–45. · Zbl 0219.90033
[5] B.C. Eaves and W.I. Zangwill, ”Generalised cutting plane methods”,SIAM Journal of Control 9 (1971) 529–542.
[6] A.M. Frieze, ”Bottleneck linear programming”,Operational Research Quarterly 26 (1975) 871–874. · Zbl 0312.90035
[7] A.M. Geoffrion, ”Duality in nonlinear programming”,SIAM Review 13 (1971) 1–37. · Zbl 0232.90049
[8] F. Glover, ”Surrogate constraints”,Operations Research 16 (1968) 741–749. · Zbl 0165.22602
[9] F. Glover, ”Surrogate constraint duality in mathematical programming”,Operations Research 23 (1975) 434–451. · Zbl 0314.90093
[10] H.J. Greenberg and W.P. Pierskalla, ”Surrogate mathematical programs”,Operations Research 18 (1970) 924–939. · Zbl 0232.90059
[11] H.J. Greenberg and W. P. Pierskalla, ”A review of quasi-convex functions”,Operations Research 19 (1971) 1553–1570. · Zbl 0228.26012
[12] H.J. Greenberg and W.P. Pierskalla, ”Quasi-conjugate functions and surrogate duality”,Cahiers du Center d’Etudes de Recherche Operationelle 15 (1973) 437–448. · Zbl 0276.90051
[13] H.J. Greenberg, ”The generalised penalty function surrogate model”,Operations Research 21 (1973) 162–178. · Zbl 0261.90056
[14] M. Held, P. Wolfe and H.P. Crowder, ”A validation of subgradient optimisation”,Mathematical Programming 6 (1974) 62–88. · Zbl 0284.90057
[15] M.H. Karwan, ”Surrogate constraint duality and extensions in integer programming”, Ph.D. dissertation, Georgia Institute of Technology (1976).
[16] M.H. Karwan and R.L. Rardin, ”Surrogate dual multiplier search procedures”, Industrial andSystems Engineering Report Series No. J-76-29, Georgia Institute of Technology, GA (1976). · Zbl 0538.90060
[17] M.H. Karwan and R.L. Rardin, ”Some relationships between Lagrangian and surrogate duality in integer linear programming”,Mathematical Programming 17 (1979) 320–334. · Zbl 0421.90056
[18] M.H. Karwan and R.L. Rardin, ”Surrogate duality in a branch-and-bound procedure”,Naval Research Logistics Quarterly (to appear). · Zbl 0453.90065
[19] M.H. Karwan and R.L. Rardin, ”Searchability of the composite and multiple surrogate dual functions”,Operations Research (to appear). · Zbl 0449.90068
[20] D.G. Luenberger, ”Quasi-convex programming”,SIAM Journal of Applied Mathematics 16 (1968) 1090–1095. · Zbl 0212.23905
[21] T.L. Magnanti, J.F. Shapiro and M.H. Wagner, ”Generalised programming solves the dual”,Management Science 22 (1976) 1195–1203. · Zbl 0352.90059
[22] T.H. Mattheiss and W.B. Widhelm, ”The generalized slack variable linear program”,Management Science 23 (1977) 859–871. · Zbl 0394.90059
[23] G.L. Nemhauser and W.B. Widhelm, ”A modified linear program for columnar methods in mathematical programming”,Operations Research 19 (1971) 1051–1060. · Zbl 0223.90018
[24] R.P. O’Neill and W.B. Widhelm, ”Computational experience with normed and non-normed column generation procedures in nonlinear programming”,Operations Research 23 (1975) 372–382. · Zbl 0309.90045
[25] B.T. Polyak, ”A general method of solving extremal problems”,Doklady Akademii Nauk SSSR 174 (1967) 33–36. · Zbl 0177.15102
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.