Stochastic Optimization Problems with Incomplete Information on Distribution Functions

Ermoliev, Y.; Gaivoronski, Alexei A.; Nedeva, C.

doi:10.1137/0323044

Cited by 74 publications

(29 citation statements)

References 10 publications

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“…Therefore, in this work we will mostly be interested in solving the DRSP model. This model was first presented by Scarf (1958) in the context of an inventory management problem and since then has been referred to as minimax stochastic programming (e.g., Dupacová (1980), Shapiro and Kleywegt (2002)), optimization with incomplete or limited distribution information (e.g., Ermoliev et al (1985)) and more recently as distributionally robust optimization. Its main application have focused stochastic linear programming with or without chance constraints as in Calafiore and El Ghaoui (2006) and in Chen et al (2007).…”

Section: Introductionmentioning

confidence: 99%

Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems

Delage

2010

Operations Research

1,544

1,209

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Stochastic programs can effectively describe the decision-making problem in an uncertain environment. Unfortunately, such programs are often computationally demanding to solve. In addition, their solutions can be misleading when there is ambiguity in the choice of a distribution for the random parameters. In this paper, we propose a model describing one's uncertainty in both the distribution's form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance). We demonstrate that for a wide range of cost functions the associated distributionally robust stochastic program can be solved efficiently. Furthermore, by deriving new confidence regions for the mean and covariance of a random vector, we provide probabilistic arguments for using our model in problems that rely heavily on historical data. This is confirmed in a practical example of portfolio selection, where our framework leads to better performing policies on the "true" distribution underlying the daily return of assets.

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Section: Introductionmentioning

confidence: 99%

Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems

Delage

2010

Operations Research

1,544

1,209

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“…The worst-case approach to decision analysis, of course, is not new. It was also discussed extensively in the stochastic programming literature (e.g., [15,16,19,22,38,48]). Again we are facing the question of how to choose the set P of possible distributions.…”

Section: Introductionmentioning

confidence: 99%

On Complexity of Stochastic Programming Problems

Shapiro

Nemirovski

Applied Optimization

245

194

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The main focus of this paper is in a discussion of complexity of stochastic programming problems. We argue that two-stage (linear) stochastic programming problems with recourse can be solved with a reasonable accuracy by using Monte Carlo sampling techniques, while multi-stage stochastic programs, in general, are intractable. We also discuss complexity of chance constrained problems and multi-stage stochastic programs with linear decision rules.

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“…These problems can be classified as belonging to a special class of stochastic optimization problems, namely optimization problems in the space of probability measures, see Karlin and Studden (1966), Kemperman (1968), Dupačová (1978), Ermoliev et al (1986), Gaivoronski (1986). One may object that to solve such problems should be even more difficult than to compute the value of F (x, H) for a given H, a difficult problem by itself as argued above.…”

Section: Technological Levelmentioning

confidence: 99%

“…The properties of (7) with the sets G j defined by (9) are well understood. Its solution has a special structure which was exploited for development of numerical methods in Ermoliev et al (1986), Gaivoronski (1986). Sometimes it is possible to obtain an explicit solution as in the important case when G j (a j ) is defined by the values of peak and average bandwidth only:…”

Section: Access Engineering Of Broadband Multiservice Networkmentioning

confidence: 99%

32. Stochastic Optimization Problems in Telecommunications

Gaivoronski

2005

Applications of Stochastic Programming

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We survey different optimization problems under uncertainty which arise in telecommunications. Three levels of decisions are distinguished: design of structural elements of telecommunication networks, top level design of telecommunication networks and design of optimal policies of telecommunication enterprize. Examples of typical problems from each level show that the stochastic programming paradigm is a powerful approach for solving telecommunication design problems.

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Stochastic Optimization Problems with Incomplete Information on Distribution Functions

Cited by 74 publications

References 10 publications

Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems

Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems

On Complexity of Stochastic Programming Problems

32. Stochastic Optimization Problems in Telecommunications

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