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Optimization Under Uncertainty

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Introduction to Applied Optimization

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Bibliography

  1. ASPEN (1982),ASPEN Technical Reference Manual, Cambridge, MA.

    Google Scholar 

  2. Beale E.M. L. (1955), On minimizing a convex function subject to linear inequalities,Journal of the Royal Statistical Society,17B, 173.

    MathSciNet  Google Scholar 

  3. Birge J. R. (1997), Stochastic programming computation and applications,INFORMS Journal on Computing,9(2),111.

    Article  MATH  MathSciNet  Google Scholar 

  4. Birge J. R. and F. Louveaux (1997),Introduction to Stochastic Programming, Springer Series in Operations Research, Springer, New York.

    MATH  Google Scholar 

  5. Charnes A. and W. W. Cooper (1959), Chance-constrained programming,Management Science,5, 73.

    Article  MathSciNet  Google Scholar 

  6. Chaudhuri P. (1996),Process synthesis under uncertainty, Ph.D. Thesis, Department of Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA .

    Google Scholar 

  7. Chaudhuri P. and U. M. Diwekar (1996), Synthesis under uncertainty: A penalty function approach,AIChE Journal,42, 742.

    Article  Google Scholar 

  8. Chaudhuri P. and U. Diwekar (1999), Synthesis approach to optimal waste blend under uncertainty,AIChE Journal,45, 1671.

    Article  Google Scholar 

  9. Dantzig G. B. (1955), Linear programming under uncertainty,Management Science,1, 197.

    Article  MATH  MathSciNet  Google Scholar 

  10. Dantzig G. B. and P. Glynn (1990), Parallel processors for planning under uncertainty,Annals of Operations Research,22, 1.

    Article  MATH  MathSciNet  Google Scholar 

  11. Dantzig G. B. and G. Infanger (1991), Large scale stochastic linear programs–Importance sampling and bender decomposition,Computational and Applied Mathematics, Brezinski and U. Kulisch (ed.), 111.

    Google Scholar 

  12. Dantzig G. B. and P. Wolfe (1960), The decomposition principle for linear programs,Operations Research,8, 101.

    Article  MATH  Google Scholar 

  13. Diwekar U. M. (1995), A process analysis approach to pollution prevention,AIChE Symposium Series on Pollution Prevention Through Process and Product Modifications,90, 168.

    Google Scholar 

  14. Diwekar U. (2003), A novel sampling approach to combinatorial optimization under uncertainty,Computational Optimization and Applications,24, 335.

    Article  MATH  MathSciNet  Google Scholar 

  15. Diwekar U. M. and J. R. Kalagnanam (1997), An efficient sampling technique for optimization under uncertainty,AIChE Journal,43, 440.

    Article  Google Scholar 

  16. Diwekar U. M. and E. S. Rubin (1994), Parameter design method using Stochastic Optimization with ASPEN,Industrial Engineering Chemistry Research,33, 292.

    Article  Google Scholar 

  17. Diwekar U. M. and E.S. Rubin (1991), Stochastic modeling of chemical Processes,Computers and Chemical Engineering,15, 105.

    Article  Google Scholar 

  18. Edgeworth E. (1888), The mathematical theory of banking,J. Royal Statistical Society,51, 113.

    Google Scholar 

  19. Higle J. and S. Sen (1991), Stochastic decomposition: An algorithm for two stage linear programs with recourse,Mathematics of Operations Research,16, 650.

    Article  MATH  MathSciNet  Google Scholar 

  20. Hopkins, D. F., M. Hoza, and C. A. Lo Presti (1994),FY94 Optimal Waste Loading Models Development, Report prepared for U.S. Department of Energy under contract DE-AC06-76RLO 1830.

    Google Scholar 

  21. Illman D. L. (1993), Researchers take up environmental challenge at Hanford,Chemical and Engineering News,9, July 21.

    Google Scholar 

  22. Iman R. L. and W. J. Conover (1982), Small sample sensitivity analysis techniques for computer models, with an application to risk assessment,Communications in Statistics,A17, 1749.

    Google Scholar 

  23. Iman R. L. and J. C. Helton (1988), An investigation of uncertainty and sensitivity analysis techniques for computer models,Risk Analysis,8(1), 71.

    Article  Google Scholar 

  24. Iman R. L. and M. J. Shortencarier(1984), A FORTRAN77 Program and User’s Guide for Generation of Latin Hypercube and Random Samples for Use with Computer Models,NUREG/CR-3624, SAND83-2365, Sandia National Laboratories, Albuquerque, N.M.

    Google Scholar 

  25. James B. A. P., Variance reduction techniques (1985),Journal of the Operations Research Society,36(6), 525.

    Google Scholar 

  26. Luckacs E. (1960),Characteristic Functions, Charles Griffin, London.

    Google Scholar 

  27. Kalagnanam J. R. and U. M. Diwekar (1997), An efficient sampling technique for off-line quality control,Technometrics,39(3), 308.

    Article  MATH  Google Scholar 

  28. Knuth D. E. (1973),The Art of Computer Programming, Volume 1: Fundamental Algorithms, Addison-Wesley, Reading, MA.

    Google Scholar 

  29. Madansky A.(1960), Inequalities for stochastic linear programming problems,Management Science,6, 197.

    Article  MATH  MathSciNet  Google Scholar 

  30. McKay M. D., R. J. Beckman, and W. J. Conover (1979), A comparison of three methods of selecting values of input variables in the analysis of output from a computer code,Technometrics,21(2), 239.

    Article  MATH  MathSciNet  Google Scholar 

  31. Milton J. S. and J. C. Arnold (1995),Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences, McGraw-Hill, New York.

    Google Scholar 

  32. Morgan G. and M. Henrion (1990),Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis, Cambridge University Press, Cambridge, UK.

    Google Scholar 

  33. Narayan, V., U. Diwekar and M. Hoza (1996), Synthesizing optimal waste blends,Industrial and Engineering Chemistry Research,35, 3519.

    Article  Google Scholar 

  34. Nemhauser, G. L., A. H. G. Ronnooy Kan, and M. J. Todd (1989),Optimization: Handbooks in operations research and management science, Vol. 1. North-Holland Press, New York.

    Google Scholar 

  35. Niederreiter H. (1992),Random Number Generation and Quasi-Monte Carlo methods, SIAM, Philadelphia.

    MATH  Google Scholar 

  36. Painton L. A. and U. M. Diwekar (1995), Stochastic annealing under uncertainty,European Journal of Operations Research,83, 489.

    Article  MATH  Google Scholar 

  37. Petruzzi N. C. and M. Dada (1999), Pricing and the newsvendor problem: A review with extensions,Operations Research,47(2), 183.

    Article  MATH  Google Scholar 

  38. Prékopa A. (1980), Logarithmic concave measures and related topics, inStochastic Programming, M. A. H. Dempster (ed.), Academic Press, New York.

    Google Scholar 

  39. Prékopa A. (1995),Stochastic Programming, Kluwer Academic, Dordrecht, Netherlands.

    Google Scholar 

  40. Raiffa H. and R. Schlaifer (1961),Applied Statistical Decision Theory, Harvard University, Boston.

    Google Scholar 

  41. Saliby E. (1990), Descriptive sampling: A better approach to Monte Carlo simulations,Journal of the Operations Research Society,41(12), 1133.

    Google Scholar 

  42. Taguchi G. (1986),Introduction to Quality Engineering, Asian Productivity Center, Tokyo.

    Google Scholar 

  43. Tintner G. (1955), Stochastic linear programming with applications to agricultural economics,Proc. 2nd Symp. Lin. Progr., Washington, 197.

    Google Scholar 

  44. Vajda S. (1972),Probabilistic Programming, Academic Press, New York.

    Google Scholar 

  45. Van Slyke R. and R. J. B. Wets (1969), L-shaped linear programs with application to optimal control and stochastic programming,SIAM Journal on Applied Mathematics,17, 638.

    Article  MATH  MathSciNet  Google Scholar 

  46. Wets R. J. B (1996), Challenges in stochastic programming,Math. Progr.,75, 115.

    MATH  MathSciNet  Google Scholar 

  47. Wets R. J. B. (1990), Stochastic programming, inOptimization Handbooks in Operations Research and Management Science, Volume 1, G. L. Nemhauser, A. H. G. Rinooy Kan, and M. J. Todd, (ed.), North-Holland, Amsterdam (1990).

    Google Scholar 

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Diwekar, U. (2008). Optimization Under Uncertainty. In: Introduction to Applied Optimization. Springer Optimization and Its Applications(), vol 22. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-76635-5_5

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