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We study singular perturbations of a class of two-scale stochastic control systems with unbounded data. The assumptions are designed to cover some relaxation problems for deep neural networks. We construct effective Hamiltonian and initial…

Optimization and Control · Mathematics 2023-03-29 Martino Bardi , Hicham Kouhkouh

This paper is concerned with first- and second-order optimality conditions as well as the stability for non-smooth semilinear optimal control problems involving the $L^1$-norm of the control in the cost functional. In addition to the…

Optimization and Control · Mathematics 2023-10-18 Vu Huu Nhu , Phan Quang Sang

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional)…

Optimization and Control · Mathematics 2011-02-11 M. J. Cánovas , M. A. LóPez , B. S. Mordukhovich , J. Parra

We provide a duality result linking the value function for a control problem with supremum cost H under an isoperimetric inequality G $\le$ gmax, and the value function for the same controlled dynamics with cost G and state constraint H…

Optimization and Control · Mathematics 2023-05-05 Dan Goreac , Alain Rapaport

We study the problem of controlling the initial condition of a vibrating beam. The optimal control problem seeks to determine solutions of initial velocity that assure the approach of the state of the beam to a given target function in the…

Optimization and Control · Mathematics 2025-02-10 Yesim Akbulut , Bismark Singh

This paper investigates strong metric subregularity around a reference point as introduced by H. Gfrerer and J. V. Outrata. In the setting of Banach spaces, we analyse its stability under Lipschitz continuous perturbations and establish its…

Optimization and Control · Mathematics 2025-05-07 Tomáš Roubal

An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…

Optimization and Control · Mathematics 2018-09-11 Sebastian Engel , Karl Kunisch

A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space.…

Optimization and Control · Mathematics 2019-11-20 Christian Clason , Yu Deng , Patrick Mehlitz , Uwe Prüfert

This paper is concerned with the stochastic recursive optimal control problem with mixed delay. The connection between Pontryagin's maximum principle and Bellman's dynamic programming principle is discussed. Without containing any…

Optimization and Control · Mathematics 2019-12-24 Weijun Meng , Jingtao Shi

We extend the classical concepts of sampling and Euler solutions for control systems associated to discontinuous feedbacks by considering also the corresponding costs. In particular, we introduce the notions of Sample and Euler…

Optimization and Control · Mathematics 2020-04-24 Anna Chiara Lai , Monica Motta

The Lipschitz constant is an important quantity that arises in analysing the convergence of gradient-based optimization methods. It is generally unclear how to estimate the Lipschitz constant of a complex model. Thus, this paper studies an…

Machine Learning · Statistics 2023-02-10 Calypso Herrera , Florian Krach , Josef Teichmann

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…

Numerical Analysis · Mathematics 2014-06-11 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu , Otmar Scherzer

In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. One of the core questions for an analysis of a model is the…

Functional Analysis · Mathematics 2022-11-22 Vít Musil , Luboš Pick , Jakub Takáč

We study a controlled version of the Bayesian sequential testing problem for the drift of a Wiener process, in which the observer exercises discretion over the signal intensity. This control incurs a running cost that reflects the resource…

Optimization and Control · Mathematics 2025-09-24 Steven Campbell , Georgy Gaitsgori , Richard Groenewald

We consider an elliptic operator $L$ with variable, merely bounded, and measurable coefficients on a Lipschitz domain, and study solutions to $Lu=0$ that attain given Neumann and Dirichlet-regularity data on different parts of the boundary.…

Analysis of PDEs · Mathematics 2026-04-24 Hongjie Dong , Martin Ulmer

We consider image registration as an optimal control problem using an optical flow formulation, i.e., we discuss an optimization problem that is governed by a linear hyperbolic transport equation. Requiring Lipschitz continuity of the…

Optimization and Control · Mathematics 2026-02-03 Johannes Haubner , Christian Clason

We provide a control-theoretic perspective on optimal tensor algorithms for minimizing a convex function in a finite-dimensional Euclidean space. Given a function $\Phi: \mathbb{R}^d \rightarrow \mathbb{R}$ that is convex and twice…

Optimization and Control · Mathematics 2026-01-21 Tianyi Lin , Michael. I. Jordan

In this paper we study the inverse boundary value problem of determining the potential in the Schr\"{o}dinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that,…

Analysis of PDEs · Mathematics 2012-11-29 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu

This article addresses control problems for semilinear impulsive neutral integro-differential equations with memory in a Banach space. It investigates the approximate controllability of linear and semilinear systems and proves the…

Optimization and Control · Mathematics 2025-07-23 Garima Gupta , Jaydev Dabas

In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…

Optimization and Control · Mathematics 2023-11-27 Stephan Dempe , Markus Friedemann , Felix Harder , Patrick Mehlitz , Gerd Wachsmuth