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Bot, Radu Ioan; Lorenz, Nicole; Wanka, Gert : Chance-constrained optimization problems and applications

Bot, Radu Ioan ; Lorenz, Nicole ; Wanka, Gert : Chance-constrained optimization problems and applications

Author(s):
Bot, Radu Ioan
Lorenz, Nicole
Wanka, Gert
Title:
Chance-constrained optimization problems and applications
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 14, 2007
Mathematics Subject Classification:
46N10 [ Applications in optimization, convex analysis, mathematical programming, economics ]
49N15 [ Duality theory ]
90C46 [ Optimality conditions, duality ]
Abstract:
In this paper we deal with chance-constrained optimization problems, a class of problems which arise naturally in practical applications in finance, engingeering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving its deterministic equivalent formulation we construct a conjugate dual problem to it and give sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also treat as an application a portfolio optimization problem for which we derive necessary and sufficient optimality conditions by means of the duality theory.
Keywords:
stochastic programming, conjugate duality, optimality conditions, chance-constraints, portfolio optimization
Language:
English
Publication time:
9 / 2007