Related papers: Optimal design with uncertainties: a risk-averse a…
We describe the numerical scheme for the discretization and solution of 2D elliptic equations with strongly varying piecewise constant coefficients arising in the stochastic homogenization of multiscale composite materials. An efficient…
Production planning must account for uncertainty in a production system, arising from fluctuating demand forecasts. Therefore, this article focuses on the integration of updated customer demand into the rolling horizon planning cycle. We…
Trajectory optimization under uncertainty underpins a wide range of applications in robotics. However, existing methods are limited in terms of reasoning about sources of epistemic and aleatoric uncertainty, space and time correlations,…
We study derivative-free methods for policy optimization over the class of linear policies. We focus on characterizing the convergence rate of these methods when applied to linear-quadratic systems, and study various settings of driving…
We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a…
We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…
We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss…
Designing high-performance electric machines that maintain their efficiency and reliability under uncertain material and operating conditions is crucial for industrial applications. In this paper, we present a novel framework for robust…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
Robust optimization is a method for optimization under uncertainties in engineering systems and designs for applications ranging from aeronautics to nuclear. In a robust design process, parameter variability (or uncertainty) is incorporated…
Conditional Value at Risk (CVaR) is a prominent risk measure that is being used extensively in various domains. We develop a new formula for the gradient of the CVaR in the form of a conditional expectation. Based on this formula, we…
The selection of optimal design for power electronic converter parameters involves balancing efficiency and thermal constraints to ensure high performance without compromising safety. This paper introduces a probabilistic-learning-based…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
We study a risk-constrained version of the stochastic shortest path (SSP) problem, where the risk measure considered is Conditional Value-at-Risk (CVaR). We propose two algorithms that obtain a locally risk-optimal policy by employing four…
A framework for risk-averse optimization problems is introduced that is resilient to ambiguities in the true form of the underlying probability distribution. The focus is on problems with partial differential equations (PDEs) as…
This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but…
This paper deals with the applications of stochastic spectral methods for structural topology optimization in the presence of uncertainties. A non-intrusive polynomial chaos expansion is integrated into a topology optimization algorithm to…