Quadratic resource allocation with generalized upper bounds

Operations Research Letters

Volumn 20, Issue 2, 1997, Pages 51-57

  Bretthauer, Kurt M ^a   Shetty, Bala ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Generalized upper bound (GUB) constraints; Nonlinear programming; Nonlinear resource allocation; Quadratic programming

Indexed keywords

CONSTRAINT THEORY; LAGRANGE MULTIPLIERS; NONLINEAR PROGRAMMING; OPTIMIZATION; RESOURCE ALLOCATION; SET THEORY;

GENERALIZED UPPER BOUND CONSTRAINTS; QUADRATIC PROGRAMMING; QUADRATIC RESOURCE ALLOCATION;

ALGORITHMS;

EID: 0031075148     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-6377(96)00039-9     Document Type: Article

References (21)

1. M.S. Bazaraa, H.D. Sherali and C.M. Shetty, Nonlinear Programming: Theory and Algorithms, 2nd ed., Wiley, New York, 1993.
2. P. Berman, N. Kovoor and P.M. Pardalos, "Algorithms for the least distance problem", in: Complexity in Numerical Optimization, (World Scientific, Singapore, 1993) 33-56.
3. G.R. Bitran and A.C. Hax, "Disaggregation and resource allocation using convex knapsack problems with bounded variables", Management Sci. 27, 431-441 (1981).
4. P. Brucker, "An O(n) algorithm for quadratic knapsack problems", Oper. Res. Lett. 3, 163-166 (1984).
5. M. Djerdjour, K. Mathur and H.M. Salkin, "A surrogate relaxation based algorithm for a general quadratic multidimensional knapsack problem", Oper. Res. Lett. 7, 253-258 (1988).
6. J.M. Farvolden, W.B. Powell and I.J. Lustig, "A primal partitioning solution for the arc-chain formulation of a multicommodity network flow problem", Oper. Res. 41, 669-693 (1993).
7. A. Federgruen and P. Zipkin, "Solution techniques for some allocation problems", Math. Programming 25, 13-24 (1983).
8. R. Helgason, J. Kennington and H. Lall, "A polynomially bounded algorithm for a singly constrained quadratic program", Math. Programming 18, 338-343 (1980).
9. D.S. Hochbaum and S. P. Hong, "About strongly polynomial time algorithms for quadratic optimization over submodular constraints", Math. Programming 69, 269-309 (1995).
10. T. Ibaraki and N. Katoh, Resource Allocation Problems, MIT Press, Cambridge, 1988.
11. J. Kennington and R. Helgason, Algorithms for Network Programming, Wiley, New York, 1980.
12. H. Luss and S.K. Gupta, "Allocation of effort resources among competing activities", Oper. Res. 23, 360-366 (1975).
13. K. Mathur, H.M. Salkin and S. Morito, "A branch and search algorithm for a class of nonlinear knapsack problems", Oper. Res. Lett. 2, 155-160 (1983).
14. N. Megiddo and A. Tamir, "Linear time algorithms for some separable quadratic programming problems", Oper. Res. Lett. 13, 203-211 (1993).
15. B.A. Murtagh and M.A. Saunders, "MINOS 5.1 User's Guide", Technical Report SOL 83-20R, Systems Optimization Laboratory, Stanford University, Standford, CA, December 1983, Revised January 1987.
16. S.S. Nielsen and S.A. Zenios, "Massively parallel algorithms for singly constrained convex programs", ORSA J. Comput. 4, 166-181 (1992).
17. P.M. Pardalos and N. Kovoor, "An algorithm for a singly constrained class of quadratic programs subject to upper and lower bounds", Math. Programming 46, 321-328 (1990).
18. P.M. Pardalos, Y. Ye and C.G. Han, "Algorithms for the solution of quadratic knapsack problems", Linear Algebra Appl. 152, 69-91 (1991).
19. A.G. Robinson, N. Jiang and C.S. Lerme, "On the continuous quadratic knapsack problem", Math. Programming 55, 99-108 (1992).
20. B. Shetty and R. Muthukrishnan, "A parallel projection for the multicommodity network model", J. Oper. Res. Soc. 41, 837-842 (1990).
21. S. Smith and L. Lasdon, "Solving large sparse non-linear programs using GRG", ORSA J. Comput. 4, 2-15 (1992).