Name
Title | ||
|---|---|---|
A probabilistic ellipsoid algorithm for linear optimization problems with uncertain LMI constraints |
Abstract | ||
|---|---|---|
In this paper, a probabilistic algorithm based on the deep cut ellipsoid method is proposed to solve a linear optimization problem subject to an uncertain linear matrix inequality (LMI). First, a deep cut ellipsoid algorithm is introduced to address probabilistic feasibility of the uncertain LMI. Objective cuts are then defined to search for the optimal solution. The final probabilistic ellipsoid algorithm is a combination of feasibility cuts and objective cuts. It is shown that in a finite number of iterations, the ellipsoid algorithm either returns a suboptimal probabilistically feasible solution with a high confidence level or finds the problem infeasible. Furthermore, the bounds of the suboptimal value are provided with probabilistic guarantees. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.automatica.2014.11.010 | Automatica |
Keywords | Field | DocType |
Linear matrix inequalities,Randomized algorithms,Uncertain systems,Ellipsoid algorithm | Linear optimization problem,Randomized algorithm,Mathematical optimization,Finite set,Control theory,Linear programming,Probabilistic logic,Uncertain systems,Ellipsoid method,Linear matrix inequality,Mathematics | Journal |
Volume | Issue | ISSN |
52 | C | 0005-1098 |
Citations | PageRank | References |
0 | 0.34 | 14 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Armin Ataei-Esfahani | 1 | 0 | 0.34 |
| Qian Wang | 2 | 184 | 12.32 |