Variable fixing algorithms for the continuous quadratic knapsack problem

Journal of Optimization Theory and Applications

Volumn 136, Issue 3, 2008, Pages 445-458

  Kiwiel, K C ^a  

^a SYSTEMS RESEARCH INSTITUTE   (Poland)

Author keywords

Convex programming; Nonlinear programming; Quadratic programming; Separable programming; Singly constrained quadratic programs

Indexed keywords

COMBINATORIAL OPTIMIZATION; QUADRATIC PROGRAMMING;

COMPUTATIONAL RESULTS; CONVERGENCE ANALYSIS; FIXING METHODS; LARGE-SCALE PROBLEM; QUADRATIC KNAPSACK PROBLEMS; QUADRATIC PROGRAMS; SEPARABLE PROGRAMMING; SINGLY-CONSTRAINED QUADRATIC PROGRAM; VARIABLE FIXING;

CONVEX OPTIMIZATION;

EID: 39749183371     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-007-9317-7     Document Type: Article

References (25)

1. Bitran, G.R., Hax, A.C.: Disaggregation and resource allocation using convex knapsack problems with bounded variables. Manag. Sci. 27, 431-441 (1981)
2. Bretthauer, K.M., Shetty, B.: Quadratic resource allocation with generalized upper bounds. Oper. Res. Lett. 20, 51-57 (1997)
3. Hochbaum, D.S., Hong, S.P.: About strongly polynomial time algorithms for quadratic optimization over submodular constraints. Math. Program. 69, 269-309 (1995)
4. Ventura, J.A.: Computational development of a Lagrangian dual approach for quadratic networks. Networks 21, 469-485 (1991)
5. Cosares, S., Hochbaum, D.S.: Strongly polynomial algorithms for the quadratic transportation problem with a fixed number of sources. Math. Oper. Res. 19, 94-111 (1994)
6. Helgason, K., Kennington, J., Lall, H.: A polynomially bounded algorithm for a singly-constrained quadratic program. Math. Program. 18, 338-343 (1980)
7. Nielsen, S.S., Zenios, S.A.: Massively parallel algorithms for singly-constrained convex programs. ORSA J. Comput. 4, 166-181 (1992)
8. Shetty, B., Muthukrishnan, R.: A parallel projection for the multicommodity network model. J. Oper. Res. Soc. 41, 837-842 (1990)
9. Cottle, R.W., Duvall, S.G., Zikan, K.: A Lagrangian relaxation algorithm for the constrained matrix problem. Nav. Res. Logist. Q. 33, 55-76 (1986)
10. Bretthauer, K.M., Shetty, B., Syam, S.: A branch-and-bound algorithm for integer quadratic knapsack problems. ORSA J. Comput. 7, 109-116 (1995)
11. Bretthauer, K.M., Shetty, B., Syam, S.: A projection method for the integer quadratic knapsack problem. J. Oper. Res. Soc. 47, 457-462 (1996)
12. Held, M., Wolfe, P., Crowder, H.P.: Validation of subgradient optimization. Math. Program. 6, 62-88 (1974)
13. Calamai, P.H., Moré, J.J.: Quasi-Newton updates with bounds. SIAM J. Numer. Anal. 24, 1434-1441 (1987)
14. Brucker, P.: An O(n) algorithm for quadratic knapsack problems. Oper. Res. Lett. 3, 163-166 (1984)
15. n. Oper. Res. Lett. 8, 219-222 (1989)
16. Pardalos, P.M., Kovoor, N.: An algorithm for a singly-constrained class of quadratic programs subject to upper and lower bounds. Math. Program. 46, 321-328 (1990)
17. n. RAIRO Rech. Opér. 31, 7-16 (1997)
18. n. J. Optim. Theory Appl. 117, 553-574 (2003)
19. Kiwiel, K.C.: On linear-time algorithms for the continuous quadratic knapsack problem. J. Optim. Theory Appl. 133, 549-554 (2007)
20. Bitran, G.R., Hax, A.C.: On the solution of convex knapsack problems with bounded variables. In: Prékopa, A. (ed.) Survey of Mathematical Programming, vol. 1, pp. 357-367. North-Holland and Akadémiai Kiadó, Amsterdam and Budapest (1979)
21. Shor, N.Z.: Minimization Methods for Nondifferentiable Functions (in Russian). Naukova Dumka, Kiev (1979). English Translation by Springer, Berlin, Germany, 1985
22. n. J. Optim. Theory Appl. 50, 195-200 (1986)
23. Robinson, A.G., Jiang, N., Lerme, C.S.: On the continuous quadratic knapsack problem. Math. Program. 55, 99-108 (1992)
24. Luss, H., Gupta, S.K.: Allocation of effort resources among competing activities. Oper. Res. 23, 360-366 (1975)
25. Kiwiel, K.C.: On Floyd and Rivest's select algorithm. Theor. Comput. Sci. 347, 214-238 (2005)