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Journal of Optimization Theory and Applications

, Volume 55, Issue 3, pp 377–390 | Cite as

On properties of the probabilistic constrained linear programming problem and its dual

  • É. Komáromi
Contributed Papers

Abstract

In this paper, the two problems inf{inf{cx:xRn,A1xy,A2xb}:y ∈ suppFRm,F(y)≥p} and sup{inf{uy:y ∈ suppFRm,F(y)≥p}+vb:uA1+vA2=c, (u,v≥0} are investigated, whereA1,A2,b,c are given matrices and vectors of finite dimension,F is the joint probability distribution of the random variables β1,...,βm, and 0<p<1. The first problem was introduced as the deterministic equivalent and the second problem was introduced as the dual of the probabilistic constrained linear programming problem inf{cx:P(A1x≥β)≥p,A2xb}.b}. Properties of the sets and the functions involved in the two problems and regularity conditions of optimality are discussed.

Key Words

Stochastic programming probabilistic constrained problems chance constrained problems duality optimization 

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References

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Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • É. Komáromi
    • 1
  1. 1.Department of Decision AnalysisNational Management Development CenterBudapestHungary

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