TY - GEN
T1 - Robust and chance-constrained optimization under polynomial uncertainty
AU - Dabbene, F.
AU - Feng, C.
AU - Lagoa, C. M.
PY - 2009
Y1 - 2009
N2 - A chance-constrained optimization problem, induced from a robust design problem with polynomial dependence on the uncertainties, is, in general, non-convex and difficult to solve. By introducing a novel concept - the kinship function - an easily computable convex relaxation of this problem is proposed. In particular, optimal polynomial kinship functions, which can be computed a priori and once for all, are introduced and used to bound the probability of constraint violation. Moreover, it is proven that the solution of the relaxed problem converges to that of the original robust optimization problem as the degree of the polynomial kinship function increases. Finally, by relying on quadrature formulae for computation of integrals of polynomials, it is shown that the computational complexity of the proposed approach is polynomial on the number of uncertainty parameters.
AB - A chance-constrained optimization problem, induced from a robust design problem with polynomial dependence on the uncertainties, is, in general, non-convex and difficult to solve. By introducing a novel concept - the kinship function - an easily computable convex relaxation of this problem is proposed. In particular, optimal polynomial kinship functions, which can be computed a priori and once for all, are introduced and used to bound the probability of constraint violation. Moreover, it is proven that the solution of the relaxed problem converges to that of the original robust optimization problem as the degree of the polynomial kinship function increases. Finally, by relying on quadrature formulae for computation of integrals of polynomials, it is shown that the computational complexity of the proposed approach is polynomial on the number of uncertainty parameters.
UR - http://www.scopus.com/inward/record.url?scp=70449672717&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70449672717&partnerID=8YFLogxK
U2 - 10.1109/ACC.2009.5160248
DO - 10.1109/ACC.2009.5160248
M3 - Conference contribution
AN - SCOPUS:70449672717
SN - 9781424445240
T3 - Proceedings of the American Control Conference
SP - 379
EP - 384
BT - 2009 American Control Conference, ACC 2009
T2 - 2009 American Control Conference, ACC 2009
Y2 - 10 June 2009 through 12 June 2009
ER -