A branch-reduce-cut algorithm for the global optimization of probabilistically constrained linear programs

DOI10.1007/s10107-006-0725-5zbMath1130.90374OpenAlexW1973769789MaRDI QIDQ2502217

Shabbir Ahmed, Faiz A. Al-Khayyal, Myun Seok Cheon

Publication date: 12 September 2006

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10107-006-0725-5

zbMATH Keywords

global optimizationbranch-and-boundchance constrained programsprobabilistically constrained linear programs

Mathematics Subject Classification ID

Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Stochastic programming (90C15) Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) (90C08)

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Uses Software

• BARON
• LINDO
• LINGO

Cites Work

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• Relaxations for probabilistically constrained programs with discrete random variables
• Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra
• Global optimization by monotonic transformation
• Designing robust emergency medical service via stochastic programming
• Convexification and global optimization in continuous and mixed-integer nonlinear programming. Theory, algorithms, software, and applications
• On convex probabilistic programming with discrete distributions.
• Introduction to global optimization
• BARON: A general purpose global optimization software package
• Monotonic Optimization: Problems and Solution Approaches
• Chance-Constrained Programming
• An Automatic Method of Solving Discrete Programming Problems
• Sharp Bounds on Probabilities Using Linear Programming
• The Probabilistic Set-Covering Problem
• A branch and bound method for stochastic integer problems under probabilistic constraints
• Contributions to the theory of stochastic programming
• Concavity and efficient points of discrete distributions in probabilistic programming.
• Convexification, concavification and monotonization in global optimization