TY - GEN A1 - Surowiec, Thomas A1 - Kouri, Drew T1 - Risk-Averse PDE-Constrained Optimization using the Conditional Value-at-Risk N2 - Uncertainty is inevitable when solving science and engineering application problems. In the face of uncertainty, it is essential to determine robust and risk-averse solutions. In this work, we consider a class of PDE-constrained optimization problems in which the PDE coefficients and inputs may be uncertain. We introduce two approximations for minimizing the conditional value-at-risk for such PDE-constrained optimization problems. These approximations are based on the primal and dual formulations of the conditional value-at-risk. For the primal problem, we introduce a smooth approximation of the conditional value-at-risk in order to utilize derivative-based optimization algorithms and to take advantage of the convergence properties of quadrature-based discretizations. For this smoothed conditional value-at-risk, we prove differentiability as well as consistency of our approximation. For the dual problem, we regularize the inner maximization problem, rigorously derive optimality conditions, and demonstrate the consistency of our approximation. Furthermore, we propose a fixed-point iteration that takes advantage of the structure of the regularized optimality conditions and provides a means of calculating worst-case probability distributions based on the given probability level. We conclude with numerical results. KW - PDE Optimization, Conditional Value-At-Risk, Uncertainty Quantification Y1 - 2015 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1365 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-13652 ER -