Related papers: Integer Optimal Control with Fractional Perimeter …
An open question contributed by Yu. Orlov to a recently published volume "Unsolved Problems in Mathematical Systems and Control Theory", V.D. Blondel, A. Megretski (eds), Princeton Univ. Press, 2004, concerns regularization of optimal…
A method is presented for the numerical solution of optimal boundary control problems governed by parabolic partial differential equations. The continuous space-time optimal control problem is transcribed into a sparse nonlinear programming…
The numerical analysis of a family of distributed mixed optimal control problems governed by elliptic variational inequalities (with parameter $\alpha >0$) is obtained through the finite element method when its parameter $h\rightarrow 0$.…
We investigate the hard-thresholding method applied to optimal control problems with $L^0(\Omega)$ control cost, which penalizes the measure of the support of the control. As the underlying measure space is non-atomic, arguments of…
We propose a local regularization of elliptic optimal control problems which involves the nonconvex $L^q$ fractional penalizations in the cost function. The proposed \emph{Huber type} regularization allows us to formulate the PDE…
We study the higher regularity of free boundaries in obstacle problems for integro-differential operators. Our main result establishes that, once free boundaries are $C^{1,\alpha}$, then they are $C^\infty$. This completes the study of…
The present work aims at the application of finite element discretizations to a class of equilibrium problems involving moving constraints. Therefore, a Moreau--Yosida based regularization technique, controlled by a parameter, is discussed…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We consider a numerical framework tailored to identifying optimal parameters in the context of modelling disease propagation. Our focus is on understanding the behaviour of optimisation algorithms for such problems, where the dynamics are…
We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…
We study the numerical approximation of linear-quadratic optimal control problems subject to the fractional Laplace equation with its spectral definition. We compute an approximation of the state equation using a discretization of the…
We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting, where the state is…
The problem of interest in this article is to study the (nonlocal) inverse problem of recovering a potential based on the boundary measurement associated with the fractional Schr\"{o}dinger equation. Let $0<a<1$, and $u$ solves…
We study the localization of sets with constant nonlocal mean curvature and prescribed small volume in a bounded open set with smooth boundary, proving that they are {\em sufficiently close} to critical points of a suitable non-local…
Particle Swarm Optimization technique offers optimal or suboptimal solution to multidimensional rough objective functions. In this paper, this optimization technique is used for designing fractional order PID controllers that give better…
Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of…
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…
The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of…
Fibre Bragg Gratings have become widespread measurement devices in engineering and other fields of application. In all but a few cases, the relation between cause and effect is simplified to a proportional model. However, at its…
We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the…