Robust discrete optimization and network flows

Mathematical Programming

Volumn 98, Issue 1-3, 2003, Pages 49-71

  Bertsimas, Dimitris ^a   Sim, Melvyn ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Integer programming; Network flows; Robust optimization

Indexed keywords

DEGREE OF CONSERVATISM; DISCRETE OPTIMIZATION PROBLEMS; INTEGER PROGRAMMING PROBLEMS; MINIMUM COST FLOW PROBLEM; NETWORK FLOW PROBLEMS; NETWORK FLOWS; POLYNOMIALLY SOLVABLE; ROBUST OPTIMIZATION;

INTEGER PROGRAMMING; OPTIMIZATION;

PROBLEM SOLVING;

EID: 84870613023     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-003-0396-4     Document Type: Conference Paper

References (18)

1. Ahuja, R., Magnanti, T., Orlin, J.: Network flows: theory, algorithms, and applications. Prentice Hall, NewYork. 1993
2. Averbakh, I.: On the complexity of a class of combinatorial optimization problems with uncertainty. Math. Prog. 90, 263-272 (2001)
3. Ben-Tal, A., Nemirovski, A.: Robust solutions of linear programming problems contaminated with uncertain data. Math. Prog. 88, 411-424 (2000)
4. Ben-Tal, A., Nemirovski, A.: Robust solutions to uncertain programs. Oper. Res. Lett. 25, 1-13 (1999)
5. Ben-Tal, A., Nemirovski, A.: Robust convex optimization. Math. Oper. Res. 23, 769-805 (1998)
6. Ben-Tal, A., El-Ghaoui, L., Nemirovski, A.: Robust semidefinite programming. In: Saigal, R., Van-denberghe, L., Wolkowicz, H., (eds), Semidefinite Programming and Applications, Kluwer Academic Publishers, 2000
7. Bertsimas, D., Sim, M.: The Price of Robustness. Working Paper, Operations Research Center, MIT, 2001
8. Birge, J.R.: The value of the stochastic solutions in stochastic linear programs with fixed recourse. Math. Prog. 24, 314-325 (1982)
9. Dantzig, G.B.: Linear programming under uncertainty. Mgmt. Sci. 197-206 (1955)
10. Dijkstra, E.W.: A note on two problems in connection with graphs. Numer. Math. 269-271 (1959)
11. El-Ghaoui, Lebret, H.: Robust solutions to least-square problems to uncertain data matrices. SIAM J. Matrix Anal. Appl. 18, 1035-1064 (1997)
12. El-Ghaoui, L., Oustry, F., Lebret, H.: Robust solutions to uncertain semidefinite programs. SIAM J. Optim. 9, 33-52 (1998)
13. Kouvelis, P., Yu, G.: Robust discrete optimization and its applications. Kluwer Academic Publishers, Norwell, MA, 1997
14. Mulvey, J.M., Vanderbei, R.J., Zenios, S.A.: Robust optimization of large-scale systems. Oper. Res. 43, 264-281 (1995)
15. Nemhauser, G., Wolsey, L.: Integer and combinatorial optimization. John Wiley and Sons, New York. 1988
16. Schultz, R., Stougie, L., van der Vlerk, M.: Solving stochastic programs with complete integer recourse by enumeration: a framework using Grobner basis reductions. Math. Prog. 83, 229-252 (1998)
17. Soyster, A.L.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21, 1154-1157 (1973)
18. Srinivasan, V., Thompson, G.L.: An operator theory of parametric programming for the transportation problem. Naval Research Logistics Quarterly 19, 205-252 (1972)