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Extremum Problems with Probability Functions: Kernel Type Solution Methods

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Encyclopedia of Optimization

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References

  1. Charnes A, Cooper WW (1959) Chance-constrained programming. Managem Sci 5:73–79

    MathSciNet  Google Scholar 

  2. Kelly J (1956) A new interpretation of information rate. Bell System Techn J 35:917–926

    Google Scholar 

  3. Kibzun AI, Kan YS (1995) Stochastic programming problems with probability and quantile functions. Wiley, New York

    Google Scholar 

  4. Kibzun A, Uryasev S (1998) Differentiability of probability functions. Stochastic Anal Appl 16:1101–1128

    Article  MATH  MathSciNet  Google Scholar 

  5. Lepp R (1979) Maximization of a probability function over simple sets (in Russian). Proc Acad Sci Estonian SSR Phys Math 28:303–308

    MATH  MathSciNet  Google Scholar 

  6. Lepp R (1980) Minimization of a smooth function over probabilistic constraints (in Russian). Proc Acad Sci Estonian SSR Phys Math 29:140–144

    MATH  MathSciNet  Google Scholar 

  7. Lepp R (1983) Stochastic approximation type algorithm for the maximization of the probability function. Proc Acad Sci Estonian SSR Phys Math 32:150–156

    MATH  MathSciNet  Google Scholar 

  8. Miele A, Cragg EG, Iver RR, Levy AV (1971) Use of the augmented penalty functions in mathematical programming problems. Part I. J Optim Th Appl 8:115–130

    Article  Google Scholar 

  9. Nurminskii EA (1979) Numerical methods for solution of deterministic and stochastic Minimax Problems. Nauk. Dumka, Kiev

    Google Scholar 

  10. Parzen E (1962) On the estimation of a probability density and the mode. Ann Math Statist 33:1065–1076

    Article  MATH  MathSciNet  Google Scholar 

  11. Polyak BT, Tsypkin YZ (1979) Adaptive algorithms of estimation (convergence, optimality, stability) (in Russian). Avtomatika i Telemekhanika (Automatics and Remote Control):74–84

    Google Scholar 

  12. Prékopa A (1980) Logarithmic concave measures and related topics. In: Dempster MAH (ed) Stochastic Programming. Acad. Press, New York

    Google Scholar 

  13. Raik E (1975) Differentiability in the parameter of the probability function and optimization of the probability function via the stochastic pseudogradient method. Proc Acad Sci Estonian SSR Phys Math 24:3–6 (In Russian.)

    MATH  MathSciNet  Google Scholar 

  14. Rosenblatt M (1957) Remarks on some nonparametric estimates of a density function. Ann Math Statist 27:832–837

    Article  MathSciNet  Google Scholar 

  15. Tamm E (1979) On the minimization of the probability function (in Russian). Proc Acad Sci Estonian SSR Phys Math 28:17–24

    MATH  MathSciNet  Google Scholar 

  16. Uryasev S (1989) A differentiation formula for integrals over sets given by inclusion. Numer Funct Anal Optim 10:827–841

    Article  MathSciNet  Google Scholar 

  17. Zangwill WI (1969) Nonlinear programming. A unified approach. Prentice-Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Tallinn Technical University, Tallinn, Estonia

    Riho Lepp

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  1. Riho Lepp
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Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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© 2008 Springer-Verlag

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Lepp, R. (2008). Extremum Problems with Probability Functions: Kernel Type Solution Methods . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_170

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