Risk Assessment for Sparse Optimization with Relaxation

Abstract

Sparse optimization with uncertainty is a widely accepted methodology that allows one to obtain robust feasible solution and then conduct sparse decision-making. To alleviate the conservative solution for robust counterpart, a probabilistic problem setup for uncertain parameter is employed to assess the risk level for the candidate solutions. Therefore, a chance constrained sparse optimization problem is well-defined that can not only measure the sparse cost but also evaluate the risk of constraints violation. In this context, we are interested in making a trade-off bridge between the sparse cost and the risk level by relaxing the constraint violations. We then shift the idea from a relaxed sparse convex optimization to risk-aware sparse optimal control application.