DUALITY FOR LINEAR CHANCE-CONSTRAINED OPTIMIZATION PROBLEMS
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
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.
참고문헌 (18)
- F. M. Allen, "Distribution-free approximations for chance constraints", Oper. Res., 22(3), pp.610~621 (1974)
- R. I. Bot, "Some new Farkas-type results for inequality systems with DC functions", J. Global Optim., 39(4), pp.595~608 (2007)
- R. I. Bot, "Dual Representations for Convex Risk Measures via Conjugate Duality", Journal of Optimization Theory and Applications (2009)
- "An exact solution approach for portfolio optimization problems under stochastic and integer constraints"[URL]
- G. Calafiore, "On distributionally robust chance-constrained linear programs", J. Optim. Theory Appl., 130(1), pp.1~22 (2006)
- A. Charnes, "Chance-constrained programming", Management Sci., 6, pp.73~79 (1959)
- A. Charnes, "Deterministic equivalents for optimizing and satisficing under chance constraints", Oper. Res., 11, pp.18~39 (1963)
- A. Charnes, "Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil", Management Sci., 4(3), pp.235~263 (1958)
- W. K. K. Haneveld, "Integrated chance constraints: reduced forms and an algorithm", Comput. Manag. Sci., 3(4), pp.245~269 (2006)
- R. Henrion, "Structural properties of linear probabilistic constraints", Optimization, 56(4), pp.425~440 (2007)
- P. Kall, "Stochastic programming" (1994), John Wiley & Sons
- S. Kataoka, "A stochastic programming model", Econometrica, 31, pp.181~196 (1963)
- C. M. Lagoa, "Probabilistically constrained linear programs and risk-adjusted controller design", SIAM J. Optim., 15(3), pp.938~951 (2005)
- A. Pr´ekopa, "Stochastic Programming" (1995), Kluwer Academic Publishers
- R. T. Rockafellar, "Convex Analysis" (1970), Princeton University Press
- A. Ruszczynski, "Stochastic Programming, Handbooks in Operations Research and Management Science, Vol. 10" (2003), Elsevier
- C. H. Scott, "On duality for square root convex programs", Math. Methods Oper. Res., 65(1), pp.75~84 (2007)
- C. van de Panne, "Minimum-cost cattle feed under probabilistic protein constraints", Management Sci., 9(3), pp.405~430 (1963)