.png){kind=icon}
Return
A probabilistic ellipsoid algorithm for linear optimization problems with uncertain LMI constraints
.png){kind=icon}
PRE
AI
DOI：10.1016/j.automatica.2014.11.010.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
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. (C) 2014 Elsevier Ltd. All rights reserved.
Keywords:
Linear matrix inequalities
Randomized algorithms
Uncertain systems
Ellipsoid algorithm
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
5.9
Papers:
1.2W
Citations:
5.2W
Organization
Cited Papers
ShareSavePolynomial-time algorithms for probabilistic solutions of parameter-dependent linear matrix inequalities.png)
AUTOMATICA
AUTOMATICAIF5.9
PREAI
ShareSaveShareSaveA probabilistic analytic center cutting plane method for feasibility of uncertain LMlsAUTOMATICA
OAAI
AUTOMATICAIF5.9
OAAIShareSaveStochastic ellipsoid methods for robust control: Multiple updates and multiple cutsAUTOMATICA
AUTOMATICAIF5.9
PREAI
ShareSaveShareSave
View more