On stochastic linear programming problems with the quantile criterion

Наумов, А. В.; Ivanov, Sergey V.

doi:10.1134/s0005117911020123

Cited by 11 publications

(10 citation statements)

References 6 publications

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“…Considering also thatX satisfies (13), we obtain H X H X j j ( ) (~) * = "Î j J k . Hence,X satisfies condition (12). The corollary has been proved.…”

Section: Theorem 3 If Conditions (4) Are Satisfied Andmentioning

confidence: 65%

“…However, C X A A A C X ( ) ( ) (8) and (11) are satisfied, then any minimal of problem (10) satisfies condition (12). .…”

Section: Theorem 3 If Conditions (4) Are Satisfied Andmentioning

confidence: 94%

“…However, wide bibliography is devoted to solving optimization problems with regard for various types of uncertainty, including probabilistic one [8][9][10][11][12][13]. These trends are combined, for example, in [14][15][16][17], where the solution of combinatorial optimization problems with interval or fuzzy uncertainty is considered.…”

Section: Introductionmentioning

confidence: 99%

“…In constructing models of stochastic optimization problems, the question arises: which solution can be considered feasible and how the best solution can be determined? There are different approaches to forming both conditions and criteria: rigid statements [9,10], probabilistic constraints and quantile optimization [11,12], models with statistical conditions [10], search of extremum of the expectation of function value, minimization of the deviation of objective function from a preset value, etc.…”

Section: Introductionmentioning

confidence: 99%

“…As above, we assume that s is determined from the condition h s + > 1 k , the set G i are equal to each other, from condition(12) it follows that for the minimal X * of problem (…”

mentioning

confidence: 99%

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Properties of the Linear Unconditional Problem of Combinatorial Optimization on Arrangements Under Probabilistic Uncertainty

Iemets

Barbolina

2016

Cybern Syst Anal

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The paper establishes the necessary condition for the solution of a linear unconditional problem of combinatorial optimization on arrangements where coefficients of objective function are positive. These results are used to establish the properties of the solution of linear unconditional optimization problem on arrangements for the case where probabilistic uncertainty takes place in the definition of the feasible domain and the minimum is defined according to the linear order introduced on the set of discrete random variables: we formulate and prove the condition that can underlie the search for solution and the ways of constructing the solution in some special cases.

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“…Considering also thatX satisfies (13), we obtain H X H X j j ( ) (~) * = "Î j J k . Hence,X satisfies condition (12). The corollary has been proved.…”

Section: Theorem 3 If Conditions (4) Are Satisfied Andmentioning

confidence: 65%

“…However, C X A A A C X ( ) ( ) (8) and (11) are satisfied, then any minimal of problem (10) satisfies condition (12). .…”

Section: Theorem 3 If Conditions (4) Are Satisfied Andmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…As above, we assume that s is determined from the condition h s + > 1 k , the set G i are equal to each other, from condition(12) it follows that for the minimal X * of problem (…”

mentioning

confidence: 99%

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