TY - GEN
T1 - An Ellipsoid Algorithm for linear optimization with uncertain LMI constraints
AU - Ataei, Armin
AU - Wang, Qian
PY - 2012
Y1 - 2012
N2 - In this paper, an efficient algorithm based on the ellipsoid method is proposed to solve a linear optimization problem over a set of uncertain Linear Matrix Inequalities (LMIs). First, an Ellipsoid Algorithm (EA) with deep cuts is introduced for solving the set of uncertain LMIs. The proposed ellipsoid algorithm is shown to converge to a probabilistically feasible point with high confidence level and in fewer iterations compared to other EA methods. Then, through a set of new cuts, the objective function is minimized while maintaining the probabilistic feasibility of the solution.
AB - In this paper, an efficient algorithm based on the ellipsoid method is proposed to solve a linear optimization problem over a set of uncertain Linear Matrix Inequalities (LMIs). First, an Ellipsoid Algorithm (EA) with deep cuts is introduced for solving the set of uncertain LMIs. The proposed ellipsoid algorithm is shown to converge to a probabilistically feasible point with high confidence level and in fewer iterations compared to other EA methods. Then, through a set of new cuts, the objective function is minimized while maintaining the probabilistic feasibility of the solution.
UR - http://www.scopus.com/inward/record.url?scp=84869473162&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84869473162&partnerID=8YFLogxK
U2 - 10.1109/acc.2012.6315611
DO - 10.1109/acc.2012.6315611
M3 - Conference contribution
AN - SCOPUS:84869473162
SN - 9781457710957
T3 - Proceedings of the American Control Conference
SP - 857
EP - 862
BT - 2012 American Control Conference, ACC 2012
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2012 American Control Conference, ACC 2012
Y2 - 27 June 2012 through 29 June 2012
ER -