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In this paper, we are interested in the analysis of a well-known free boundary/shape optimization problem motivated by some issues arising in population dynamics. The question is to determine optimal spatial arrangements of favorable and…
In this paper we consider an optimal control problem (OCP) for the coupled system of a nonlinear monotone Dirichlet problem with matrix- valued non-smooth controls in coefficients and a nonlinear equation of Ham- merstein type. Since…
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…
We would like to study the solution stability of a parametric control problem governed by semilinear elliptic equations with a mixed state-control constraint, where the cost function is nonconvex and the admissible set is unbounded. The…
Given an optimal control problem on a heterogeneous body with a periodical structure of particles depending on a small parameter e, we study the asymptotic behavior, as e converges to zero, of the optimal control functional and the optimal…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear parabolic equations. We consider the reconstruction of the full solution of the parabolic equation posed in $\Omega\times (0,T)$ -…
We consider a family of optimal control problems where the control variable is given by a boundary condition of Neumann type. This family is governed by parabolic variational inequalities of the second kind. We prove the strong convergence…
We propose a general framework for studying optimal impulse control problem in the presence of uncertainty on the parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the…
We address the slow convergence and poor stability of quasi-newton sequential quadratic programming (SQP) methods that is observed when solving experimental design problems, in particular when they are large. Our findings suggest that this…
We study the ultraviolet problem for models of a finite-dimensional quantum mechanical system linearly coupled to a bosonic quantum field, such as the (many-)spin boson model or its rotating-wave approximation. If the state change of the…
We study a stochastic optimal control problem with the state constrained to a smooth, compact domain. The control influences both the drift and a possibly degenerate, control-dependent dispersion matrix, leading to a fully nonlinear,…
This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…
Here we derive a nonsmooth maximum principle for optimal control problems with both state and mixed constraints. Crucial to our development is a convexity assumption on the "velocity set". The approach consists of applying known…
Parabolic equations on evolving domains model a multitude of applications including various industrial processes such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations…
We investigate fast and communication-efficient algorithms for the classic problem of minimizing a sum of strongly convex and smooth functions that are distributed among $n$ different nodes, which can communicate using a limited number of…
Optimal control problems involving hybrid binary-continuous control costs are challenging due to their lack of convexity and weak lower semicontinuity. Replacing such costs with their convex relaxation leads to a primal-dual optimality…
This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on…