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The paper presents an approach to studying optimal control problems in the space of nonnegative measures with dynamics given by a nonlocal balance law. This approach relies on transforming the balance law into a continuity equation in the…

Optimization and Control · Mathematics 2025-01-30 Nikolay Pogodaev , Maxim Staritsyn

We consider a heat conduction problem $S$ with mixed boundary conditions in a n-dimensional domain $\Omega$ with regular boundary $\Gamma$ and a family of problems $S_{\alpha}$, where the parameter $\alpha>0$ is the heat transfer…

Optimization and Control · Mathematics 2019-12-20 Domingo A. Tarzia , Carolina M. Bollo , Claudia M. Gariboldi

We consider nonsmooth optimal control problems subject to a linear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. It is well-known that local solutions satisfy the celebrated Pontryagin maximum…

Optimization and Control · Mathematics 2024-06-28 Daniel Wachsmuth

We consider a heat conduction problem $S$ with mixed boundary conditions in a $n$-dimensional domain $\Omega$ with regular boundary and a family of problems $S_{\alpha}$ with also mixed boundary conditions in $\Omega$, where $\alpha>0$ is…

Optimization and Control · Mathematics 2021-03-30 C. M. Bollo , C. M. Gariboldi , D. A. Tarzia

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

This paper is concerned with the optimal control problem governed by a linear parabolic equation and subjected to box constraints on control variables. This type of problem has important applications in heating and cooling systems. By…

Optimization and Control · Mathematics 2022-04-04 Hailing Wang , Changjun Yu , Di Wu

We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…

Analysis of PDEs · Mathematics 2023-09-13 Rinaldo M. Colombo , Elena Rossi

In this paper we use a Stackelberg-Nash strategy to show the local null controllability of a parabolic equation where the diffusion coefficient is the product of a degenerate function in space and a nonlocal term. We consider one control…

Optimization and Control · Mathematics 2025-09-25 Juan Límaco , João Carlos Barreira , Suerlan Silva , Luis P. Yapu

We consider a steady-state heat conduction problem in a multidimensional bounded domain Omega for the Poisson equation with constant internal energy g and mixed boundary conditions given by a constant temperature b in the portion Gamma_1 of…

Optimization and Control · Mathematics 2020-04-06 Julieta Bollati , Claudia M. Gariboldi , Domingo A. Tarzia

Recent studies utilize multiple kernel learning to deal with incomplete-data problem. In this study, we introduce new methods that do not only complete multiple incomplete kernel matrices simultaneously, but also allow control of the…

Machine Learning · Computer Science 2018-12-26 Rachelle Rivero , Tsuyoshi Kato

Finite element approximations of Dirichlet boundary control problems governed by parabolic PDEs on convex polygonal domains are studied in this paper. The existence of a unique solution to optimal control problems is guaranteed based on…

Optimization and Control · Mathematics 2014-10-02 Wei Gong , Michael Hinze , Zhaojie Zhou

In this paper we study we study a Dirichlet optimal control prob- lem associated with a linear elliptic equation the coefficients of which we take as controls in the class of integrable functions. The characteristic feature of this control…

Optimization and Control · Mathematics 2015-10-30 Thierry Horsin , Peter Kogut , Olivier Wilk

In this contribution we study the singular limit problem of a nonlocal conservation law with a discontinuity in space. The specific choice of the nonlocal kernel involving the spatial discontinuity as well enables it to obtain a maximum…

Analysis of PDEs · Mathematics 2022-12-27 Alexander Keimer , Lukas Pflug

Optimal control of a mobile robot system is formulated. Multiobjective criteria of time and energy is employed. The optimal control problem is formulated as a nonlinear programming problem (NLP). The problem is solved using the direct…

Optimization and Control · Mathematics 2013-12-30 Mohamad Shahab , Amar Khoukhi , Fouad Al-Sunni

In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…

Numerical Analysis · Mathematics 2023-06-07 Wei Gong , Zhiyu Tan

In this paper we deal with the well-posedness of Dirichlet problems associated to nonlocal Hamilton-Jacobi parabolic equations in a bounded, smooth domain $\Omega$, in the case when the classical boundary condition may be lost. We address…

Analysis of PDEs · Mathematics 2014-05-01 Guy Barles , Erwin Topp

In this paper we consider a linear hybrid system which composed by two non-homogeneous rods connected by a point mass and generated by the equation\bea\left\{ \begin{array}{ll} \rho_{1}(x)u_{t}=(\sigma_{1}(x)u_{x})_{x}-q_{1}(x)u,&…

Optimization and Control · Mathematics 2017-03-09 Jamel Ben Amara , Hedi Bouzidi

Recently, several works have been carried out in attempt to develop a theory for linear or sublinear elliptic equations involving a general class of nonlocal operators characterized by mild assumptions on the associated Green kernel. In…

Analysis of PDEs · Mathematics 2022-05-20 Phuoc-Truong Huynh , Phuoc-Tai Nguyen

We consider an optimal control problem governed by a class of boundary value problem with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes is stated. The proof of the main result…

Analysis of PDEs · Mathematics 2017-12-29 Dorota Bors

In this paper, we recover the boundary null controllability for the degenerate heat equation by analyzing the asymptotic behavior of an eligible family of state-control pairs $((u_{\varepsilon}, h_{\varepsilon}))_{\varepsilon >0}$ solving…

Optimization and Control · Mathematics 2022-02-08 Bruno Sérgio V. Araújo , Reginaldo Demarque , Luiz Viana