TY - CONF
T1 - Random convex approximations of ambiguous chance constrained programs
T2 - 2016 IEEE 55th Conference on Decision and Control (CDC)
Y1 - 2016/12//
SP - 6210
EP - 6215
A1 - Tseng, Shih-Hao
A1 - Eilyan Bitar
A1 - Tang, Ao
KW - RM14-002
AB - We investigate an approach to the approximation of ambiguous chance constrained programs (ACCP) in which the underlying distribution describing the random parameters is itself uncertain. We model this uncertainty with the assumption that the unknown distribution belongs to a closed ball centered around a fixed and known distribution. Using only samples drawn from the central distribution, we approximate ACCP with a robust sampled convex program (RSCP), and establish an upper bound on the probability that a solution to the RSCP violates the original ambiguous chance constraint, when the uncertainty set is defined in terms of the Prokhorov metric. Our bound on the constraint violation probability improves upon the existing bounds for RSCPs in the literature. We also consider another approach to approximating ACCP by means of a sampled convex program (SCP), which is built on samples drawn from the central distribution. Again, we provide upper bounds on the probability that a solution to the SCP violates the original ambiguous chance constraint for uncertainty sets defined according to a variety of metrics.
JF - 2016 IEEE 55th Conference on Decision and Control (CDC)
PB - IEEE
CY - Las Vegas, NV, USA
DO - 10.1109/CDC.2016.7799224
ER -