Related papers: A path-following inexact Newton method for PDE-con…
In this paper, an inexact Newton method for solving real-valued nonlinear eigenvalue problems with eigenvector dependency (NEPv) is introduced that is able to solve the problem on a matrix level. Our main contribution is to derive a variant…
This study proposes a cubic regularization of the Newton method for generating weakly efficient points of unconstrained vector optimization problems under no convexity assumption on the objective function. It is observed that at a given…
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…
This thesis investigates optimal trajectory tracking of nonlinear dynamical systems with affine controls. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. The concept of…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
In this paper a special piecewise linear system is studied. It is shown that, under a mild assumption, the semi-smooth Newton method applied to this system is well defined and the method generates a sequence that converges linearly to a…
We study physics-informed neural networks (PINNs) as numerical tools for the optimal control of semilinear partial differential equations. We first recall the classical direct and indirect viewpoints for optimal control of PDEs, and then…
We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following…
In this paper we study a distributed optimal control problem for a nonlocal convective Cahn--Hilliard equation with degenerate mobility and singular potential in three dimensions of space. While the cost functional is of standard tracking…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
We study an explicit mirror-descent method for finite-horizon deterministic optimal control problems. The method is motivated by Pontryagin's maximum principle: at each iteration, one solves the state and adjoint equations and updates the…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…
We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…
We consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage…
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.…
Identifying the discontinuous diffusion coefficient in an elliptic equation with observation data of the gradient of the solution is an important nonlinear and ill-posed inverse problem. Models with total variational (TV) regularization…
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…
A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…
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…