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We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…

Optimization and Control · Mathematics 2025-10-17 Michael Kartmann , Stefan Volkwein

In this paper we prove the existence of an optimal domain which minimizes the buckling load of a clamped plate among all bounded domains with given measure. Instead of treating this variational problem with a volume constraint, we introduce…

Optimization and Control · Mathematics 2021-10-07 Kathrin Stollenwerk

We investigate a shape optimization problem for a heat-conducting fluid governed by a Boussinesq system. The main goal is to determine an optimal domain shape that yields a temperature distribution as uniform as possible. Initially, we…

Analysis of PDEs · Mathematics 2025-04-23 Andrea Ceretani , Weiwei Hu , Lin Mu , Carlos Rautenberg

In this paper, we study a shape optimization problem for the torsional energy associated with a domain contained in an infinite cylinder, under a volume constraint. We prove that a minimizer exists for all fixed volumes and show some of its…

Analysis of PDEs · Mathematics 2025-08-06 Paolo Caldiroli , Alessandro Iacopetti , Filomena Pacella

We consider a bilinear optimal control problem with pointwise tracking for a semilinear elliptic PDE in two and three dimensions. The control variable enters the PDE as a (reaction) coefficient and the cost functional contains point…

Optimization and Control · Mathematics 2025-12-16 Enrique Otarola , Daniel Quero , Matias Sasso

Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…

Optimization and Control · Mathematics 2014-12-10 Harbir Antil , Shawn W. Walker

In this paper we develop necessary conditions for optimality, in the form of the Pontryagin maximum principle, for the optimal control problem of a class of infinite dimensional evolution equations with delay in the state. In the cost…

Probability · Mathematics 2017-06-12 Giuseppina Guatteri , Federica Masiero , Carlo Orrieri

In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…

Optimization and Control · Mathematics 2020-06-15 Martin Gugat , Michael Schuster , Enrique Zuazua

We consider an optimal control problem for a non-autonomous model of ODEs that describes the evolution of the number of customers in some firm. Namely we study the best marketing strategy. Considering a $L^2$ cost functional, we establish…

Optimization and Control · Mathematics 2018-02-16 S. Rosa , P. Rebelo , C. M. Silva , H. Alves , P. G. Carvalho

The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…

Optimization and Control · Mathematics 2022-05-03 Cornel Marius Murea , Dan Tiba

This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…

Optimization and Control · Mathematics 2017-02-24 Andrew Lamperski , Khem Raj Ghusinga , Abhyudai Singh

Relying on the careful study of a related problem in the calculus of variations, we study a class of optimal control problems in which the control lies on the acceleration, with state constraints on the position variable. In dimension one,…

Optimization and Control · Mathematics 2025-10-10 Yves Achdou

Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…

Analysis of PDEs · Mathematics 2021-06-21 Stefano Almi , Ulisse Stefanelli

We study a control problem governed by a semilinear parabolic equation with pointwise control and state constraints imposed at every point of the space-time cylinder. We obtain second order sufficient optimality conditions for local…

Optimization and Control · Mathematics 2024-03-04 Eduardo Casas , Mariano Mateos , Arnd Rösch

We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…

Optimization and Control · Mathematics 2020-09-23 Martin Burger , René Pinnau , Claudia Totzeck , Oliver Tse

Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…

Optimization and Control · Mathematics 2010-10-11 Rouhollah Tavakoli

We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space $\R^N$. For such optimal control…

Analysis of PDEs · Mathematics 2014-05-06 Guy Barles , Ariela Briani , Emmanuel Chasseigne , Nicoletta Tchou

The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…

Optimization and Control · Mathematics 2012-11-19 Eveline Rosseel , Garth N. Wells

We consider an optimization problem related to elliptic PDEs of the form $-{\rm div}(a(x)\nabla u)=f$ with Dirichlet boundary condition on a given domain $\Omega$. The coefficient $a(x)$ has to be determined, in a suitable given class of…

Optimization and Control · Mathematics 2025-12-10 Giuseppe Buttazzo , Juan Casado-Díaz , Faustino Maestre

In this paper we investigate necessary conditions of optimality for infinite-horizon optimal control problems with overtaking optimality as an optimality criterion. For the case of local Lipschitz continuity of the payoff function, we…

Optimization and Control · Mathematics 2017-04-12 Dmitry Khlopin