Algorithms for the solution of stochastic dynamic minimax problems
Computational Optimization and Applications
Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
Mathematics of Operations Research
Robust Solutions to Uncertain Semidefinite Programs
SIAM Journal on Optimization
Operations Research
Adjustable robust solutions of uncertain linear programs
Mathematical Programming: Series A and B
Computational complexity of stochastic programming problems
Mathematical Programming: Series A and B
A Robust Optimization Approach to Inventory Theory
Operations Research
A Robust Optimization Perspective on Stochastic Programming
Operations Research
A Linear Decision-Based Approximation Approach to Stochastic Programming
Operations Research
Operations Research
Uncertain Linear Programs: Extended Affinely Adjustable Robust Counterparts
Operations Research
Robust Approximation to Multiperiod Inventory Management
Operations Research
Robust solutions of uncertain linear programs
Operations Research Letters
Robust Optimization Made Easy with ROME
Operations Research
A constraint sampling approach for multi-stage robust optimization
Automatica (Journal of IFAC)
A Distributional Interpretation of Robust Optimization
Mathematics of Operations Research
Distributionally Robust Markov Decision Processes
Mathematics of Operations Research
Price of Correlations in Stochastic Optimization
Operations Research
Robust Storage Assignment in Unit-Load Warehouses
Management Science
Robust Markov Decision Processes
Mathematics of Operations Research
Multiple Objectives Satisficing Under Uncertainty
Operations Research
Hi-index | 0.00 |
In this paper we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust and more flexible than the standard technique of using linear rules. Our framework begins by first affinely extending the set of primitive uncertainties to generate new linear decision rules of larger dimensions and is therefore more flexible. Next, we develop new piecewise-linear decision rules that allow a more flexible reformulation of the original problem. The reformulated problem will generally contain terms with expectations on the positive parts of the recourse variables. Finally, we convert the uncertain linear program into a deterministic convex program by constructing distributionally robust bounds on these expectations. These bounds are constructed by first using different pieces of information on the distribution of the underlying uncertainties to develop separate bounds and next integrating them into a combined bound that is better than each of the individual bounds.