Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1287/opre.1090.0795 | Operations Research |
Keywords | Field | DocType |
deterministic convex program,uncertain linear program,flexible reformulation,distributionally robust bound,distributionally robust optimization,modular framework,tractable approximations,original problem,new piecewise-linear decision rule,new linear decision rule,linear rule,linear optimization problem,stochastic,programming,piecewise linear,convex programming,decision rule,robust optimization,linear program,technology,linear optimization,operations | Linear optimization problem,Decision rule,Mathematical optimization,Robust optimization,Regular polygon,Linear programming,Modular design,Convex optimization,Approximate solution,Mathematics | Journal |
Volume | Issue | ISSN |
58 | 4-Part-1 | 0030-364X |
Citations | PageRank | References |
96 | 3.22 | 24 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Joel Goh | 1 | 164 | 9.07 |
| Melvyn Sim | 2 | 1909 | 117.68 |