Threshold value of the penalty parameter in the minimization of L-1-penalized conditional Value-at-Risk

Vladimir Gaitsgory*, Tanya Tarnopolskaya

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)191-204
Number of pages14
JournalJournal of Industrial and Management Optimization
Volume9
Issue number1
DOIs
Publication statusPublished - 2013
Externally publishedYes

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