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Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical simulation of dynamical systems as problems of Bayesian state estimation. Aside from producing posterior distributions over ODE solutions and…
This paper studies the partially observed stochastic optimal control problem for systems with state dynamics governed by partial differential equations (PDEs) that leads to an extremely large problem. First, an open-loop deterministic…
Elliptic PDE-constrained optimal control problems with $L^1$-control cost ($L^1$-EOCP) are considered. To solve $L^1$-EOCP, the primal-dual active set (PDAS) method, which is a special semismooth Newton (SSN) method, used to be a priority.…
We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterize the feasibility of…
We present a new algorithm for solving linear-quadratic regulator (LQR) problems with linear equality constraints, also known as constrained LQR (CLQR) problems. Our method's sequential runtime is linear in the number of stages and…
In this article we investigate the numerical solution of a scalar semilinear stochastic delay differential equation (SDDE) where the linear instantaneous feedback and nonlinear delayed feedback terms are perturbed by a pair of standard…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
Decentralized non-convex optimization is important in many problems of practical relevance. Existing decentralized methods, however, typically either lack convergence guarantees for general non-convex problems, or they suffer from a high…
This paper investigates a model-free solution to the stochastic linear quadratic regulation (LQR) problem for linear discrete-time systems with both multiplicative and additive noises. We formulate the stochastic LQR problem as a nonconvex…
The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE…
We propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear…
In this paper, we study an optimal control problem of linear backward stochastic differential equation (BSDE) with quadratic cost functional under partial information. This problem is solved completely and explicitly by using a stochastic…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time variant of the well-known Differential Dynamic Programming (DDP) technique with a Gauss-Newton Hessian approximation. This family of methods has gained popularity in the…
Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses…
This paper presents a review of the current state-of-the-art of numerical methods for nonlinear Dirac (NLD) equation. Several methods are extendedly proposed for the (1+1)-dimensional NLD equation with the scalar and vector self-interaction…
Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial differential equations over time. This work shows that…
We consider quadrature formulas of high order in time based on Radau-type, L-stable implicit Runge-Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs…
The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical…
Method-of-lines discretizations are demanding test problems for stiff integration methods. However, for PDE problems with known analytic solution the presence of space discretization errors or the need to use codes to compute reference…