On properties of the probabilistic constrained linear programming problem and its dual |
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Authors: | É Komáromi |
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Institution: | (1) Department of Decision Analysis, National Management Development Center, Budapest, Hungary |
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Abstract: | In this paper, the two problems inf{inf{cx:x R
n,A
1
xy,A
2
xb}:y suppF R
m,F(y)p} and sup{inf{uy:y suppF R
m,F(y)p}+vb:uA
1+vA
2=c, (u,v0} are investigated, whereA
1,A
2,b,c are given matrices and vectors of finite dimension,F is the joint probability distribution of the random variables 1,...,
m, 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(A
1
x)p,A
2
xb}.b}. Properties of the sets and the functions involved in the two problems and regularity conditions of optimality are discussed. |
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Keywords: | Stochastic programming probabilistic constrained problems chance constrained problems duality optimization |
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