Algorithm to optimize the quantile criterion for the polyhedral loss function and discrete distribution of random parameters

Ivanov, Sergey V.; Наумов, А. В.

doi:10.1134/s0005117912010080

Cited by 14 publications

(8 citation statements)

References 8 publications

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“…Let us find another bound which is better than this. For this end, we consider a more general problem than (12), in which the ball S r has center in the coordinate origin and variable radius r ∈ [ , R]:…”

Section: Reduction Of the Problem To A Sequence Of Convex Programmingmentioning

confidence: 99%

“…In the literature (Norkin , Naumov and Ivanov), the quantile optimization problem with a discrete distribution, is reduced to a mixed integer programming problem. The same method was used to reduce a chance‐constrained programming problem, which is similar to the quantile optimization problem, to a mixed integer programming problem (Sen , Ruszczyński , Benati and Rizzi , Luedtke et al ).…”

Section: Introductionmentioning

confidence: 99%

“…In particular, in Norkin , the quantile function is assumed to be uniformly bounded for all values of the strategy. A special structure of the loss function (maximum of linear functions) is used by Naumov and Ivanov to obtain an analogous result. Note also that special algorithms are applied in Norkin , Norkin and Boiko , Naumov and Ivanov , and Naumov and Bobylev to solve the equivalent problem of the mixed integer linear programming.…”

Section: Introductionmentioning

confidence: 99%

“…A special structure of the loss function (maximum of linear functions) is used by Naumov and Ivanov to obtain an analogous result. Note also that special algorithms are applied in Norkin , Norkin and Boiko , Naumov and Ivanov , and Naumov and Bobylev to solve the equivalent problem of the mixed integer linear programming. A more general case of the stochastic programming problem is considered by Kibzun et al , where the original problem is transformed into a mixed integer programming problem.…”

Section: Introductionmentioning

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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Section: Reduction Of the Problem To A Sequence Of Convex Programmingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…However, problems of this class for the quantile criterion are more difficult, because the quantile criterion is not convex in general. A stochastic programming problem with polyhedral loss function and quantile criterion is considered in [5,6]. Although the functions describing the problem are piecewise linear, it is difficult to find the value of the quantile function for an arbitrary distribution of random parameters.…”

Section: Introductionmentioning

confidence: 99%

Variable neighborhood search for stochastic linear programming problem with quantile criterion

et al. 2019

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We consider the stochastic linear programming problem with quantile criterion and continuous distribution of random parameters. Using the sample approximation, we obtain a stochastic programming problem with discrete distribution of random parameters. It is known that the solution to this problem provides an approximate solution to the problem with continuous random parameters if the size of the sample is large enough. Applying the confidence method, we reduce the problem to a mixed integer programming problem, which is linear with respect to continuous variables. Integer variables determine confidence sets, and we describe the structure of the optimal confidence set. This property allows us to take into account only confidence sets that may be optimal. To find an approximate solution to the problem, we suggest a modification of the variable neighborhood search and determine structures of neighborhoods used in the search. Also, we discuss a method to find a good initial solution and give results of numerical experiments. We apply the developed algorithm to solve a problem of optimization of a hospital budget.

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Deterministic Approximation of Stochastic Programming Problems with Probabilistic Constraints

Kan

Васильева

2019

Mathematical Optimization Theory and Operations Research

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Algorithm to optimize the quantile criterion for the polyhedral loss function and discrete distribution of random parameters

Cited by 14 publications

References 8 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

Variable neighborhood search for stochastic linear programming problem with quantile criterion

Deterministic Approximation of Stochastic Programming Problems with Probabilistic Constraints

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