The solution of groundwater quality management problems with a nonconvex feasible region using a cutting plane optimization technique

Water Resources Research

Volumn 32, Issue 4, 1996, Pages 1091-1100

  Karatzas, George P ^a   Pinder, George F ^a  

^a University of Vermont   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GROUND WATER;

ALGORITHM; AQUIFER; METHODOLOGY; UNITED STATES;

GROUNDWATER; MANAGEMENT; WATER QUALITY;

EID: 0029657372     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/95WR03812     Document Type: Article

References (18)

1. Ahlfeld, D. P., Designing contaminated groundwater remediation systems using numerical simulation and nonlinear optimization, Ph.D. dissertation, Dept. of Civ. Eng., Princeton Univ., Princeton, N. J., 1987.
2. Ahlfeld, D. P., J. M. Mulvey, G. F. Pinder, and E. F. Wood, Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory, 1, Model development, Water Resour. Res., 24(3), 431-441, 1988a.
3. Ahlfeld, D. P., J. M. Mulvey, and G. F. Pinder, Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory, 2, Analysis of a field site, Water Resour. Res., 24(3), 443-452, 1988b.
4. Avriel, M., and A. C. Williams, Complementary geometric programming, SIAM J. Appl. Math., 19, 125-141, 1970.
5. Bazaraa, M. S., and C. M. Shetty, Nonlinear Programming, John Wiley, New York, 1979.
6. Brcdehoeft, J. D., and G. F. Pinder, Mass transport in flowing groundwater, Water Resour. Res., 9(1), 194-210, 1973.
7. Hillestad, R. J., and S. E. Jacobsen, Reverse convex programming, Appl. Math. Optimization, 6, 63-78, 1980a.
8. Hillestad, R. J., and S. E. Jacobsen, Linear programs with an additional reverse convex constraint, Appl. Math. Optimization, 6, 257-269, 1980b.
9. Horst, R., Deterministic global optimization with partition sets whose feasibility is not known: Application to concave minimization, reverse convex constraints, D.C.-programming and Lipschitzian optimization, J. Optimization Theory Appl., 58, 11-37, 1988.
10. Horst, R., and H. Tuy, Global Optimization, Springer-Verlag, New York, 1990.
11. Karatzas, G. P., and G. F. Pinder, Groundwater management using numerical simulation and the outer approximation method for global optimization, Water Resour. Res., 29(10), 3371-3378, 1993.
12. Meyer, R., The validity of a family of optimization methods, J. SLAM Control, 8(1), 41-54, 1970.
13. Murtagh, B. A., and M. A. Saunders, MINOS 5.1 users guide, Tech. Rep. SOL 83-20R, Dep. of Oper. Res., Stanford Univ., Stanford, Calif., 1987.
14. Rockafellar, R. T., Convex Analysis, Princeton Univ. Press, Princeton, N. J., 1972.
15. Rosen, J. B., Iterative solutions of nonlinear optimal control problems, J. SIAM Control, 4(1), 223-244, 1966.
16. Tuy, H., Concave programming under linear constraints, Transl. Sov. Math., 5, 1437-1440, 1964.
17. Tuy, H., On outer approximation methods for solving concave minimization problems, Acta Math. Vietnamica, 8, 3-34, 1983.
18. Tuy, H., Global minimization of a difference of two convex functions, Math. Programming Study, 30, 152-182, 1987.