Quantitative stability of mixed-integer two-stage quadratic stochastic programs

For our introduced mixed-integer quadratic stochastic program with fixed recourse matrices, random recourse costs, technology matrix and right-hand sides, we study quantitative stability properties of its optimal value function and optimal solution set when the underlying probability distribution is...

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Bibliographic Details
Published in:Mathematical methods of operations research (Heidelberg, Germany) Vol. 75; no. 2; pp. 149 - 163
Main Authors: Chen, Zhiping, Han, Youpan
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.04.2012
Springer
Springer Nature B.V
Subjects:
Business and Management
Calculus of Variations and Optimal Control; Optimization
Continuity
Integer programming
Linear programming
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrices
Operations research
Operations Research/Decision Theory
Optimization
Original Article
Portfolio management
Probability distribution
Production planning
Stability
Stochasticity
Studies
Stochastic quadratic programs
Stability
Probability metric
Mixed-integer
Lipschitz continuity
ISSN:1432-2994, 1432-5217
Online Access:Get full text
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Summary:For our introduced mixed-integer quadratic stochastic program with fixed recourse matrices, random recourse costs, technology matrix and right-hand sides, we study quantitative stability properties of its optimal value function and optimal solution set when the underlying probability distribution is perturbed with respect to an appropriate probability metric. To this end, we first establish various Lipschitz continuity results about the value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of linear constraints. The obtained results extend earlier results about quantitative stability properties of stochastic integer programming and stability results for mixed-integer parametric quadratic programs.
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ISSN:1432-2994
1432-5217
DOI:10.1007/s00186-010-0326-1