Related papers: PDE-Constrained Optimization Models and Pseudospec…
In this paper we consider non convex control problems of stochastic differential equations driven by relaxed controls. We present existence of optimal controls and then develop necessary conditions of optimality. We cover both continuous…
In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few…
This paper presents a pseudo-spectral method for Dynamic Optimization Problems (DOPs) that allows for tight polynomial bounds to be achieved via flexible sub-intervals. The proposed method not only rigorously enforces inequality…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…
We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks for the continuous primal…
We introduce an efficient boundary-adapted spectral method for peridynamic diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication…
Common computational problems, such as parameter estimation in dynamic models and PDE constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive…
We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…
We present an approach to handle Dirichlet type nonlocal boundary conditions for nonlocal diffusion models with a finite range of nonlocal interactions. Our approach utilizes a linear extrapolation of prescribed boundary data. A novelty is,…
Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally…
We consider joint optimization and learning problems arising in real-time decision systems. While most existing work focuses primarily on convex, revenue-based objectives, we extend this line of research to multi-objective formulations. In…
This paper explores a fully discrete approximation for a nonlinear hyperbolic PDE-constrained optimization problem (P) with applications in acoustic full waveform inversion. The optimization problem is primarily complicated by the…
The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…
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…
This paper continues the investigations from [7] and is concerned with the derivation of first-order conditions for a control constrained optimization problem governed by a non-smooth elliptic PDE. The control enters the state equation not…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…
We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…
The well-posedness of a class of optimal control problems is analysed, where the state equation couples a nonlinear degenerate Fokker-Planck equation with a system of Ordinary Differential Equations (ODEs). Such problems naturally arise as…