Name
Title | ||
|---|---|---|
A scenario approach for estimating the suboptimality of linear decision rules in two-stage robust optimization. |
Abstract | ||
|---|---|---|
Robust dynamic optimization problems involving adaptive decisions are computationally intractable in general. Tractable upper bounding approximations can be obtained by requiring the adaptive decisions to be representable as linear decision rules (LDRs). In this paper we investigate families of tractable lower bounding approximations, which serve to estimate the degree of suboptimality of the best LDR. These approximations are obtained either by solving a dual version of the robust optimization problem in LDRs or by utilizing an inclusion-wise discrete approximation of the problem's uncertainty set. The quality of the resulting lower bounds depends on the distribution assigned to the uncertain parameters or the choice of the discretization points within the uncertainty set, respectively. We prove that identifying the best possible lower bounds is generally intractable in both cases and propose an efficient procedure to construct suboptimal lower bounds. The resulting instance-wise bounds outperform known worst-case bounds in the majority of our test cases. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/CDC.2011.6161342 | CDC-ECE |
Keywords | Field | DocType |
approximation theory,decision making,decision theory,optimisation,stability,adaptive decisions,computational intractability,decision making,discretization points,inclusion-wise discrete approximation,instance-wise bounds,linear decision rules,problems uncertainty set,robust dynamic optimization problems,suboptimal lower bounds,suboptimality estimation,tractable lower bounding approximations,tractable upper bounding approximations,two-stage robust optimization,worst-case bounds | Decision rule,Mathematical optimization,Computer science,Robust optimization,Approximation theory,Robustness (computer science),Probability distribution,Decision theory,Optimization problem,Bounding overwatch | Conference |
ISSN | Citations | PageRank |
0743-1546 | 11 | 0.54 |
References | Authors | |
9 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael J. Hadjiyiannis | 1 | 11 | 0.54 |
| Paul J. Goulart | 2 | 444 | 45.59 |
| Daniel Kuhn | 3 | 559 | 32.80 |