J. Korean Math. Soc. 2010; 47(1): 17-28
Printed January 1, 2010
https://doi.org/10.4134/JKMS.2010.47.1.17
Copyright © The Korean Mathematical Society.
Radu Ioan Bo\c t, Nicole Lorenz, and Gert Wanka
Chemnitz University of Technology
In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.
Keywords: stochastic programming, conjugate duality, optimality conditions, chance-constraints, portfolio optimization
MSC numbers: 49N15, 90C46, 46N10
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