A Bilevel Stochastic Programming Problem with Random Parameters in the Follower’s Objective Function

DOI10.1134/S1990478918040063zbMath1438.90156OpenAlexW2902579153WikidataQ128896205 ScholiaQ128896205MaRDI QIDQ4973229

Sergey V. Ivanov

Publication date: 2 December 2019

Published in: Journal of Applied and Industrial Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1990478918040063

zbMATH Keywords

stochastic programmingvalue-at-risksample average approximationbilevel problemquantile criterion

Mathematics Subject Classification ID

Decision theory (91B06) Linear programming (90C05) Stochastic programming (90C15) Management decision making, including multiple objectives (90B50)

Related Items (12)

A systematic sampling evolutionary (SSE) method for stochastic bilevel programming problems ⋮ Exact methods for discrete \({\varGamma}\)-robust interdiction problems with an application to the bilevel knapsack problem ⋮ Exploiting the polyhedral geometry of stochastic linear bilevel programming ⋮ A survey on bilevel optimization under uncertainty ⋮ A survey on mixed-integer programming techniques in bilevel optimization ⋮ Risk-Averse Models in Bilevel Stochastic Linear Programming ⋮ A robust approach for modeling limited observability in bilevel optimization ⋮ On continuity in risk-averse bilevel stochastic linear programming with random lower level objective function ⋮ Existence of solutions for a class of bilevel stochastic linear programs ⋮ On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints ⋮ Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography ⋮ Sample approximations of bilevel stochastic programming problems with probabilistic and quantile criteria

Cites Work

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• Stochastic problem of competitive location of facilities with quantile criterion
• Sample average approximation method for chance constrained programming: Theory and applications
• Practical bilevel optimization. Algorithms and applications
• Foundations of bilevel programming
• On the convergence of sample approximations for stochastic programming problems with probabilistic criteria
• Upper Bound for the Competitive Facility Location Problem with Quantile Criterion
• Variational Analysis
• Reduction of the bilevel stochastic optimization problem with quantile objective function to a mixed‐integer problem
• Bilevel Programming Problems
• Probability-1

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