Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
Uncertain convex programs: randomized solutions and confidence levels
Mathematical Programming: Series A and B
Ambiguous chance constrained problems and robust optimization
Mathematical Programming: Series A and B
Convex Approximations of Chance Constrained Programs
SIAM Journal on Optimization
Ambiguous Risk Measures and Optimal Robust Portfolios
SIAM Journal on Optimization
Convexity of chance constraints with independent random variables
Computational Optimization and Applications
A Robust Optimization Perspective on Stochastic Programming
Operations Research
On Safe Tractable Approximations of Chance-Constrained Linear Matrix Inequalities
Mathematics of Operations Research
The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs
SIAM Journal on Optimization
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This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, our approach directly uses the historical data information and leads to tighter uncertainty sets and therefore to better objective values. This improvement is significant, especially when the number of uncertain parameters is low. Other advantages of our approach are that it can handle joint chance constraints easily, it can deal with uncertain parameters that are dependent, and it can be extended to nonlinear inequalities. Several numerical examples illustrate the validity of our approach.