On Solution of Stochastic Linear Programs by Discretization Methods

  • K. Marti
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 59)


Stochastic linear programs (SLP) with complete fixed recourse are solved approximatively by means of discretization of the underlying probability distribution of the random parameters. Error estimates are given, and a priori bounds for the approximation error are derived. Furthermore, exploiting invariance properties of the probability distribution of the random parameters, problem-oriented discretizations are derived which simplify then the computation of admissible descent directions at non-stationary points.


Stochastic linear programs (SLP) discretization methods a priori error bounds invariant probability distributions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Marti, K.: Optimal design of trusses as a stochastic linear programming problem, In: A. S. Nowak (ed.). Reliability and Optimization of Structural Systems, University of Michigan Press, Ann Arbor, 1998, pp. 231–239.Google Scholar
  2. [2]
    Marti, K.: Approximationen der Entscheidungsprobleme mit linearer Ergebnisfunktion und positiv homogener, subadditiver Verlustfunktion, Z. Wahrsch. verve. Geb. 31 (1975), 203–233.MathSciNetzbMATHGoogle Scholar
  3. [3]
    Kall, P.: Stochastic Linear Programming, Springer-Verlag, Berlin, 1976.Google Scholar
  4. [4]
    Kall, P. and Wallace, S. W.: Stochastic Programming, Wiley, Chichester, 1994.Google Scholar
  5. [5]
    Mayer, J.: Stochastic Linear Programming Algorithms, Gordon and Breach, 1998.Google Scholar
  6. [6]
    Marti, K.: Entscheidungsprobleme mit linearem Aktionen-und Ergebnisraum, Z. Wahrsch. verw. Geb. 23 (1972), 133–147.CrossRefMathSciNetzbMATHGoogle Scholar
  7. [7]
    Marti, K.: Diskretisierung stochastischer Programme unter Berücksichtigung der Problemstruktur, Z. Angew. Math. Mech. 59 (1979). T105–T108.MathSciNetzbMATHGoogle Scholar
  8. [8]
    Marti, K.: Approximationen stochastischer Optimiemngsprobleme, Verlag Anton Hain Meisenheim GmbH, Königstein/Ts., 1979.Google Scholar
  9. [9]
    Marti, K.: Computation of descent directions in stochastic optimization problems with invariant distributions, Z. Angew. Math. Mech. 65 (1995). 355–378.MathSciNetGoogle Scholar
  10. [10]
    Marti, K.: Descent Directions and Efficient Solutions in Disretely Distributed Stochastic Programs, Lecture Notes in Econom. Math. Systems 299, Springer-Verlag, Berlin, 1988.Google Scholar
  11. [11]
    Marti, K.: Computation of efficient solutions of discretely distributed stochastic optimization problems, Math. Methods Oper. Res. 36 (1992), 259–294.MathSciNetzbMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • K. Marti
    • 1
  1. 1.Aero-Space Engineering and TechnologyFederal Armed Forces UniversityMünchenGermany

Personalised recommendations