Related papers: Measuring Singularity of Generalized Minimizers fo…
We study the planar least gradient problem with respect to an anisotropic norm $\phi$ for continuous boundary data. We prove existence of minimizers for strictly convex domains $\Omega$. Furthermore, we inspect the issue of uniqueness and…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
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…
We consider control constrained optimal control problems governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnetic permeability, and charge density. Moreover, the parameter…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
This paper studies regularity properties of optimization-based controllers, which are obtained by solving optimization problems where the parameter is the system state and the optimization variable is the input to the system. Under a wide…
This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality…
We investigate local optimality conditions of first and second order for integer optimal control problems with total variation regularization via a finite-dimensional switching point problem. We show the equivalence of local optimality for…
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…
In this article, we consider the Tikhonov regularization of an optimal control problem of semilinear partial differential equations with box constraints on the control. We derive a-priori regularization error estimates for the control under…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
We investigate the numerical approximation of an elliptic optimal control problem which involves a nonconvex local regularization of the $L^q$-quasinorm penalization (with $q\in(0,1)$) in the cost function. Our approach is based on the…
We consider regularity issues for minima of non-autonomous functionals in the Calculus of Variations exhibiting non-uniform ellipticity features. We provide a few sharp regularity results for local minimizers that also cover the case of…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…
We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose…
In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target…
A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…