TY - JOUR
T1 - Threshold value of the penalty parameter in the minimization of L-1-penalized conditional Value-at-Risk
AU - Gaitsgory, Vladimir
AU - Tarnopolskaya, Tanya
PY - 2013
Y1 - 2013
N2 - A problem of minimization of L1-penalized conditional value-at-risk (CVaR) is considered. It is shown that there exists a non-negative threshold value of the penalty parameter such that the optimal value of the penalized problem is unbounded if the penalty parameter is less than the threshold value, and it is bounded if the penalty parameter is greater or equal than this value. It is established that the threshold value can be found via the solution of a linear programming problem, and, therefore, readily computable. Theoretical results are illustrated by numerical examples.
AB - A problem of minimization of L1-penalized conditional value-at-risk (CVaR) is considered. It is shown that there exists a non-negative threshold value of the penalty parameter such that the optimal value of the penalized problem is unbounded if the penalty parameter is less than the threshold value, and it is bounded if the penalty parameter is greater or equal than this value. It is established that the threshold value can be found via the solution of a linear programming problem, and, therefore, readily computable. Theoretical results are illustrated by numerical examples.
UR - http://www.scopus.com/inward/record.url?scp=84875278036&partnerID=8YFLogxK
U2 - 10.3934/jimo.2013.9.191
DO - 10.3934/jimo.2013.9.191
M3 - Article
AN - SCOPUS:84875278036
SN - 1547-5816
VL - 9
SP - 191
EP - 204
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
IS - 1
ER -