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Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…
We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general…
We address a class of integer optimization programs with a total variation-like regularizer and convex, separable constraints on a graph. Our approach makes use of the Graver basis, an optimality certificate for integer programs, which we…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…
Focus of this work is solving a non-smooth constraint minimization problem by a primal-dual splitting algorithm involving proximity operators. The problem is penalized by the Bregman divergence associated with the non-smooth total variation…
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…
This paper proposes a method to compute lower performance bounds for discrete-time infinite-horizon min-max control problems with input constraints and bounded disturbances. Such bounds can be used as a performance metric for control…
This paper deals with the development and analysis of novel time-optimal point-to-point model predictive control concepts for nonlinear systems. Recent approaches in the literature apply a time transformation, however, which do not maintain…
We show how the solution to NMPC problems for a special type of input-affine discrete-time systems can be obtained by reformulating the underlying non-convex optimal control problem in terms of a finite number of convex subproblems. The…
We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…
This paper presents an inverse optimality method to solve the Hamilton-Jacobi-Bellman equation for a class of nonlinear problems for which the cost is quadratic and the dynamics are affine in the input. The method is inverse optimal because…
In this paper, we investigate optimal control problems for Allen-Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace-Beltrami operator. The approach covers both the…
This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality.…
This contribution considers optimal control problems subject to nonlocal conservation laws -- those in which the velocity depends nonlocally (i.e., via a convolution) on the solution -- and the so-called singular limit. First, the existence…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…
In this paper, we address a social planner's optimal control problem for a partially observable stochastic epidemic model. The control measures include social distancing, testing, and vaccination. Using a diffusion approximation for the…