An algorithm for the inequality-constrained discrete min-max problem

SIAM Journal on Optimization

Volumn 8, Issue 1, 1998, Pages 265-283

  Rustem, Berc ^a   Nguyen, Quoc ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Adaptive penalty; Augmented Lagrangian; Convergent stepsizes; Min max; Quasi Newton algorithm; Rival scenarios

Indexed keywords

EID: 0032358586     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1056263493260386     Document Type: Article

References (31)

1. K. J. ARROW, F. J. GOULD, AND S. M. HOWE (1973), General saddle point result for constrained optimization, Math. Programming, 5, pp. 225-234.
2. K. J. ARROW AND R. M. SOLOW (1958), Gradient methods for constrained maxima, with weakened assumptions, in Studies in Linear and Nonlinear Programming, K. Arrow, L. Hurwicz, and H. Uzawa, eds., Stanford University Press, Stanford, CA, pp. 166-176.
3. J. ASAADI (1973), A computational comparison of nonlinear programs, Math. Programming, 4, pp. 144-154.
4. M. C. B. BIGGS (1974), The Development of a Class of Constrained Minimization Algorithms and their Application to the Problem of Power Scheduling, Ph.D. thesis, Department of Computer Science, Queen Mary College, University of London, London, UK.
5. C. CHARALAMBOUS AND J. W. BANDLER (1976), Nonlinear minimax optimization as a sequence of least pth optimization with finite values of p, Internat. J. Systems Sci., 7, pp. 377-394.
6. C. CHARALAMBOUS AND A. R. CONN (1978), An efficient algorithm to solve the min-max problem directly, SIAM J. Numer. Anal., 15, pp. 162-187.
7. G. C. CHOW (1979), Effective use of econometric models in macroeconomic policy formulation, in Optimal Control for Econometric Models, S. Holly, B. Rustem, and M. Zarrop, eds., Macmillan, London, pp. 31-39.
8. T. F. COLEMAN (1978), A note on "New algorithms for constrained minimax optimization," Math. Programming, 15, pp. 239-242.
9. A. R. CONN (1979), An Efficient Second Order Method to Solve the Constrained Minmax Problem, Report, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada.
10. A. R. CONN AND Y. LI (1992), A structure exploiting algorithm for nonlinear minimal problems, SIAM J. Optim., 2, pp. 242-263.
11. V. F. DEMYANOV AND V. N. MALOZEMOV (1974), Introduction to Minmax, John Wiley, New York.
12. V. F. DEMYANOV AND A. B. PEVNYI (1972), Some estimation in minmax problems, Kibernetika, 1, pp. 107-112 (in Russian).
13. S. R. K. DUTTA AND M. VIDYASAGAR (1977), New algorithms for constrained minmax optimization, Math. Programming, 13, pp. 149-155.
14. J. FUHRER AND J. HALTMAIER (1986), Minimum Variance Pooling of Forecasts at Different Levels of Aggregation, Special Studies Paper 208, Federal Reserve Board, Washington, D.C.
15. P. E. GILL, W. MURRAY, AND M. H. WRIGHT (1981), Practical Optimization, Academic Press, New York.
16. C. GRANGER AND P. NEWBOLD (1977), Forecasting Economic Time Series. Academic Press, New York.
17. J. H. HALD AND K. MADSEN (1981), Combined LP and quasi-Newton methods for minimal optimization, Math. Programming, 20, pp. 49-62.
18. S. P. HAN (1981), Variable metric methods for minimizing a class of nondifferentiable functions, Math. Programming, 20, pp. 1-13.
19. M. J. LAWRENCE, R. H. EDMUNSON, AND M. J. O'CONNOR (1986), The accuracy of combining judgmental and statistical forecasts, Management Science, 32, pp. 1521-1532.
20. S. MAKRIDAKIS AND R. WINKLER (1983), Averages of forecasts: Some empirical results, Management Science, 29, pp. 987-996.
21. W. MURRAY AND M. L. OVERTON (1980), A projected Lagrangian algorithm for nonlinear minmax optimization, SIAM J. Sci. Statist. Comput., 1, pp. 345-370.
22. E. POLAK, J. E. HIGGINS, AND D. Q. MAYNE (1992), A barrier function method for minimax problems, Math. Programming, 54, pp. 155-176.
23. E. POLAK, D. Q. MAYNE, AND J. E. HIGGINS (1991), A superlinearly convergent min-max algorithm for min-max problems, J. Optim. Theory Appl., 69, pp. 407-439.
24. E. POLAK AND A. L. TITS (1980), A globally convergent, implementable multiplier method with automatic penalty limitation, Appl. Math. Optim., 6, pp. 335-360.
25. M. J. D. POWELL (1978), A fast algorithm for nonlinearly constrained optimization problems, in Numerical Analysis, Dundee, 1977, Lecture Notes in Mathematics 630, G. A. Watson, ed., Springer-Verlag, Berlin, pp. 144-157.
26. R. T. ROCKAFELLAR (1973), A dual approach to solving nonlinear programming problems by unconstrained minimization, Math. Programming, 5, pp. 354-373.
27. B. RUSTEM (1987), Methods for the simultaneous use of multiple models in optimal policy design, in Developments in Control Theory for Economic Analysis, C. Carraro and D. Sartore, eds., Martinas Nijhoff Kluwer Publishers, Dordrecht, The Netherlands, pp. 157-186.
28. B. RUSTEM (1992), A superlinearly convergent min-max algorithm for rival models of the same economic system, Math. Programming, 53, pp. 279-295.
29. B. RUSTEM (1993), Equality and inequality constrained optimization algorithms with convergent stepsizes, J. Optim. Theory Appl., 76, pp. 429-453.
30. R. A. TAPIA (1986), On Secant Updates for Use in General Constrained Optimization, Technical report 84-3, Department of Mathematical Sciences, Rice University, Houston, TX.
31. R. S. WOMERSLEY AND R. FLETCHER (1986), An algorithm for composite nonsmooth optimization problems, J. Optim. Theory Appl., 48, pp. 493-523.