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DUALITY FOR LINEAR CHANCE-CONSTRAINED OPTIMIZATION PROBLEMS

  • Bot, Radu Ioan (Chemnitz University of Technology Faculty of Mathematics) ;
  • Lorenz, Nicole (Chemnitz University of Technology Faculty of Mathematics) ;
  • Wanka, Gert (Chemnitz University of Technology Faculty of Mathematics)
  • Published : 2010.01.01

Abstract

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.

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