Related papers: Deep Uzawa for PDE constrained optimisation
The Uzawa method is a method for solving constrained optimization problems, and is often used in computational contact mechanics. The simplicity of this method is an advantage, but its convergence is slow. This paper presents an accelerated…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…
Recently the authors have studied a state and control constrained optimal control problem with fractional elliptic PDE as constraints. The goal of this paper is to continue that program forward and introduce an algorithm to solve such…
We propose a neural network framework for solving stationary linear transport equations with inflow boundary conditions. The method represents the solution using a neural network and imposes the boundary condition via a Lagrange multiplier,…
Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
While much attention of neural network methods is devoted to high-dimensional PDE problems, in this work we consider methods designed to work for elliptic problems on domains $\Omega \subset \mathbb{R} ^d, $ $d=1,2,3$ in association with…
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
We investigate the iterative methods proposed by Maz'ya and Kozlov (see [KM1], [KM2]) for solving ill-posed inverse problems modeled by partial differential equations. We consider linear evolutionary problems of elliptic, hyperbolic and…
In this paper, elliptic control problems with integral constraint on the gradient of the state and box constraints on the control are considered. The optimal conditions of the problem are proved. To numerically solve the problem, we use the…
Many computer vision and image processing problems can be posed as solving partial differential equations (PDEs). However, designing PDE system usually requires high mathematical skills and good insight into the problems. In this paper, we…
Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…
In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…
We investigate the iterative methods proposed by Maz'ya and Kozlov (see [3], [4]) for solving ill-posed reconstruction problems modeled by PDE's. We consider linear time dependent problems of elliptic, hyperbolic and parabolic types. Each…
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…
Distributed network optimization has been studied for well over a decade. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality,…
We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve the governing equation for the control function which…