Guaranteeing approach to solving quantile optimization problems

Кибзун, А. И.; Kurbakovskiy, V. Yu.

doi:10.1007/bf02204810

Cited by 14 publications

(6 citation statements)

References 4 publications

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“…(8) Solve the linear programming problem (24), (25). Thus, we find a starting point for the problem (26).…”

Section: A Modification Of the Algorithmsmentioning

confidence: 99%

“…Thus, we find a starting point for the problem (26). (9) Further, we apply the branch and bound method to solve the integer programming problem (26), for which the values of the loss function are calculated by solving the linear programming problem (24), (25). We consider only the points x k , k ∈  S , where the set  S is defined by the formula (27).…”

Section: A Modification Of the Algorithmsmentioning

confidence: 99%

“…Recall that U is a convex polyhedron. Therefore, the problem (21) is transformed into the linear programming problem → min u∈U, ∈R 1 (24) subject to the linear constraints…”

Section: R R=1mentioning

confidence: 99%

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Comparison of two algorithms for solving a two‐stage bilinear stochastic programming problem with quantile criterion

Кибзун

2015

Appl Stoch Models Bus & Ind

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The paper is devoted to solving the two-stage problem of stochastic programming with quantile criterion. It is assumed that the loss function is bilinear in random parameters and strategies, and the random vector has a normal distribution. Two algorithms are suggested to solve the problem, and they are compared. The first algorithm is based on the reduction of the original stochastic problem to a mixed integer linear programming problem. The second algorithm is based on the reduction of the problem to a sequence of convex programming problems. Performance characteristics of both the algorithms are illustrated by an example. A modification of both the algorithms is suggested to reduce the computing time. The new algorithm uses the solution obtained by the second algorithm as a starting point for the first algorithm.

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“…(8) Solve the linear programming problem (24), (25). Thus, we find a starting point for the problem (26).…”

Section: A Modification Of the Algorithmsmentioning

confidence: 99%

Section: A Modification Of the Algorithmsmentioning

confidence: 99%

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Comparison of two algorithms for solving a two‐stage bilinear stochastic programming problem with quantile criterion

Кибзун

2015

Appl Stoch Models Bus & Ind

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“…Remark 2.7.4. Stochastic Gradient Approaches for distribution functions of the above form can be found in [124,125]. In energy applications, stochastic gradient approaches have been investigated for minimizing expected value objective functions (e.g., [59,89]).…”

Section: Special Casesmentioning

confidence: 99%

Chance-Constrained Programming

2013

Encyclopedia of Operations Research and Management Science

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In a way the basis for this thesis was laid in 2005 when together with some colleagues we were quantifying the impact of uncertainty on weekly unit-commitment. A fruitful collaboration with Pierre Thomas and Riadh Zorgati led to the birth of a software package called LEA ("Laboratoire des Expérimentations des Aléas") in the same year. From a technical perspective this software package allowed the user to execute a simple multiscenario approach around a deterministic optimization kernel. The innovating part was set up with Bernard Beauzamy. Instead of drawing scenarios as iid samples from some law (or black box software), the idea was to build artificial englobing scenarios allowing for bounding of output with only little computational effort. These experiments led, only much later, to an industrial software package. In any case this is how together with Riadh Zorgati, I got interested in dealing with uncertainty in an appropriate way. We had many discussions on Scenario generation, Robust Optimization etc These discussions were also greatly nourished by discussions with Michel Minoux. Around the same time, we had the chance to meet René Henrion and attend a seminar he gave. Chance constrained programming looked like a very powerful and intuitive way to deal with uncertainty. With good hopes and enthusiasm we set out to look where uncertainty in Energy Management plays a key role and should be dealt with appropriately. Once these structures identified we started experimenting with safe tractable approximations of chance constraints, scenario type of approaches and also Robust Optimization. Somewhere in 2009 we had to chance to work closely together with René Henrion and look to what extent Chance Constrained programming could be applied in Energy Management. This led me to be greatly intrigued by this field, and ultimately, gave me a desire to deeply understand this domain. Thanks to EDF I have had the opportunity to do this Thesis in part time. I hope to have contributed to the domain and continue to do so in the future. I do firmly believe that Chance Constrained Programming will be important in Energy Management in the near future.Thanking people after 10 years of work at EDF is almost a dangerous undertaking since we are bound to forget someone with whom we have had interesting discussions. Nonetheless I will make this attempt at my own risks.First of all I would like to thank Riadh Zorgati, who is a good friend and colleague. We share many views and in particular that (fundamental) research should have its place in an(y) industrial company. I would also like to thank Grace Doukopoulos, Olivier Feron, Nadia Oudjane, Cyrille Strugarek and Xavier Warin for the many interesting discussions (and years of joint work). Thanks to Thomas Triboulet, Laurent Mulot and their pragmatic viewpoint of what at EDF we commonly call "le métier" it is possible to obtain a partial view of the underlying structures of the optimization problems at hand. This allows for important progress in identifying the key features of Energy Ma...

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“…단,   = 번째 생산 활동(예: 쌀 식부면적),        = 번째 활동의 수익(gross margin) 2) (Charnes and Cooper, 1959;Madansky, 1962;Maruyama, 1972;Kibzun and Kurbakovskiy, 1991;Kibzun and Kan, 1996 (Hazell and Norton, 1986).…”

mentioning

confidence: 99%

Valuation of Irrigation Water: A Chance-Constrained Programming Approach

Kwon¹,

Lee²,

Heo³

2009

Journal of Korea Water Resources Association

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This study estimates the value of irrigation water in Korea using an economic programming model that is constructed with all the resource endowment constraints, technology restrictions and policy variables. The variability and uncertainty of water resource endowment are incorporated into the model through the chance-constrained technique. Solving the profit maximization problems with gradually reduced water endowments, we derive a series of shadow values of irrigation water. It has been found that uncertainty in water supply raises the damage from water loss, and the marginal damage increases in water loss.

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Guaranteeing approach to solving quantile optimization problems

Cited by 14 publications

References 4 publications

Comparison of two algorithms for solving a two‐stage bilinear stochastic programming problem with quantile criterion

Comparison of two algorithms for solving a two‐stage bilinear stochastic programming problem with quantile criterion

Chance-Constrained Programming

Valuation of Irrigation Water: A Chance-Constrained Programming Approach

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