Related papers: Local-global model reduction method for stochastic…
Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized {nonlinear} elliptic partial differential equations (PDEs). CB-pMOR is designed to deal with large-scale problems for which full-order…
A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…
This paper studies an optimal control problem for continuous-time stochastic systems subject to reachability objectives specified in a subclass of metric interval temporal logic specifications, a temporal logic with real-time constraints.…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
In the context of Galerkin discretizations of a partial differential equation (PDE), the modes of the classical method of Proper Orthogonal Decomposition (POD) can be interpreted as the ansatz and trial functions of a low-dimensional…
In this paper, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal…
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…
We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients based on model order reduction techniques and the Laplace…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
This study proposes an approach based on a perturbation technique to construct global solutions to dynamic stochastic general equilibrium models (DSGE). The main idea is to expand a solution in a series of powers of a small parameter…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…
Optimal and safety-critical control are fundamental problems for stochastic systems, and are widely considered in real-world scenarios such as robotic manipulation and autonomous driving. In this paper, we consider the problem of…
This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…
We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…
In [1] we consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization, where we provide a condition which allows to decide whether a solution of the necessary first order conditions…
To integrate strategic, tactical and operational decisions, the two-stage optimization has been widely used to guide dynamic decision making. In this paper, we study the two-stage stochastic programming for complex systems with unknown…