Topology optimization under uncertainty (TOuU) often defines objectives and constraints by
statistical moments of geometric and physical quantities of interest. Most traditional TOuU …

Models incorporating uncertain inputs, such as random forces or material parameters, have
been of increasing interest in PDE-constrained optimization. In this paper, we focus on the …

For finite-dimensional problems, stochastic approximation methods have long been used to
solve stochastic optimization problems. Their application to infinite-dimensional problems is …

In this work, we present a novel approach for solving stochastic shape optimization
problems. Our method is the extension of the classical stochastic gradient method to infinite …

Shape optimization models with one or more shapes are considered in this chapter. Of
particular interest for applications are problems in which a so-called shape functional is …

We consider an optimal control problem (OCP) for a partial differential equation (PDE) with
random coefficients. The optimal control function is a deterministic, distributed forcing term …

The primary objective of this work is to study the inverse problem of identifying a parameter
in partial differential equations with random data. We explore the nonlinear inverse problem …

An algorithm is proposed to solve robust control problems constrained by partial differential
equations with uncertain coefficients, based on the so-called MG/OPT framework. The levels …

We develop a variational inequality approach for the inverse problem of identifying a
stochastic parameter in a stochastic partial differential equation. An iteratively regularized …

In this paper we extend the adaptive gradient descent (AdaGrad) algorithm to the optimal
distributed control of parabolic partial differential equations with uncertain parameters. This …