This work highlights an approach for incorporating realistic uncertainties into scientific
computing workflows based on finite elements, focusing on prevalent applications in …

Uncertainty is prevalent in engineering design, statistical learning, and decision making
broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to …

A smooth penalty function method which does not involve dual and slack implicit variables to
formulate constrained optimization conditions is proposed. New active and loss functions …

The primary goal of this paper is to provide an efficient solution algorithm based on the
augmented Lagrangian framework for optimization problems with a stochastic objective …

Constructing accurate statistical models of critical system responses typically requires an
enormous amount of experimental data. Unfortunately, physical experimentation is often …

We apply the sample average approximation (SAA) method to risk-neutral optimization
problems governed by nonlinear partial differential equations (PDEs) with random inputs …

This article develops a new algorithm named TTRISK to solve high‐dimensional risk‐averse
optimization problems governed by differential equations (ODEs and/or partial differential …

This manuscript presents a framework for using multilevel quadrature formulae to compute
the solution of optimal control problems constrained by random partial differential equations …

In this manuscript, we present a collective multigrid algorithm to solve efficiently the large
saddle-point systems of equations that typically arise in PDE-constrained optimization under …

Control and optimization problems constrained by partial differential equations (PDEs) with
random input data and that incorporate probabilities of failure in their formulations are …