Mercator Fellow Matthias Heinkenschloss scheduled to lecture via ZOOM

 

Abstract

This talk gives a unified presentation of several recent optimization approaches for solving risk-averse partial differential equation constrained optimization problems and addresses a numerical issue that arises in (semismooth) Newton methods used to solve subproblems in each of these approaches. Risk-averse optimization problems arise, for example, in engineering applications when one seeks to maximize the performance of, or minimize the costs of a system under uncertainty. Whereas risk-neutral formulations optimize the average costs or performance, risk-averse formulations penalize high-cost, rare-events, which yield excessively high costs or low performance. Risk-averse objectives like the Conditional Value-at-Risk (CVaR) are notoriously expensive to optimize due to their non-smooth nature and the inherent expense in sampling rare-events.

This talk focusses on the CVaR risk measure and studies recent optimization approaches which either directly smooth the CVaR or are based on a reformulation as a smooth inequality constrained problem, such as log-barrier or augmented Lagrangian approaches. It is shown that all considered approaches solve the CVaR optimization problem by solving a sequence of smoothed CVaR optimization problems. Furthermore, a computationally inexpensive modification of (semismooth) Newton methods is introduced that alleviates numerical issues arising from near rank deficient Hessians and inconsistent quadratic models that can arise in the smoothed CVaR subproblems.  

 

This talk is based on joint work with Mae Markowski.