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The analysis of an optimal control problem of nonlocal type is analyzed. The results obtained are applied to the study the corresponding local optimal control problems. The state equations are governed by p-laplacian elliptic operators, of…

Analysis of PDEs · Mathematics 2020-04-07 Julio Muñoz

We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…

Optimization and Control · Mathematics 2024-08-01 Daniel Wachsmuth

In this paper, a class of semilinear fractional elliptic equations associated to the spectral fractional Dirichlet Laplace operator is considered. We establish the existence of optimal solutions as well as a minimum principle of Pontryagin…

Optimization and Control · Mathematics 2023-04-28 Cyrille Kenne , Gisèle Mophou , Mahamadi Warma

We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like penalty on the variational problem. The reformulation is an…

Numerical Analysis · Mathematics 2014-04-08 Giang Tran , Hayden Schaeffer , William M. Feldman , Stanley J. Osher

We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general…

Optimization and Control · Mathematics 2014-07-24 Mohammed Benharrat , Delfim F. M. Torres

We investigate $C^1$ finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state formulated as fourth order variational inequalities for the state…

Numerical Analysis · Mathematics 2020-06-29 Susanne C. Brenner , Li-Yeng Sung , Winnifried Wollner

We consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization. We provide a condition which allows to decide whether a solution of the necessary first order conditions is a global…

Optimization and Control · Mathematics 2015-03-25 Ahmad Ahmad Ali , Klaus Deckelnick , Michael Hinze

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…

Optimization and Control · Mathematics 2018-12-04 Shuzhen Yang

We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…

Optimization and Control · Mathematics 2013-09-10 Vladimir Gaitsgory , Ludmila Manic

An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of…

Optimization and Control · Mathematics 2010-08-20 Hongwei Lou

We will investigate the value and inactive region of optimal stopping and one-sided singular control problems by focusing on two fundamental ratios. We shall see that these ratios unambiguously characterize the solution, although usually…

Probability · Mathematics 2015-02-10 Pekka Matomäki

We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…

Optimization and Control · Mathematics 2016-06-10 Ahmad Ahmad Ali , Michael Hinze , Heiko Kröner

We geometrically describe optimal control problems in terms of Morse families in the Hamiltonian framework. These geometric structures allow us to recover the classical first order necessary conditions for optimality and the starting point…

Optimization and Control · Mathematics 2012-11-20 María Barbero-Liñán , David Iglesias Ponte , David Martín de Diego

The minimization of energy-like cost functionals is addressed in the context of optimal control problems. For a general class of dynamical systems, with possibly unstable and nonlinear free dynamics, it is shown that a sequence of solutions…

Optimization and Control · Mathematics 2022-12-06 Sérgio S. Rodrigues

In this paper we consider optimal control problems where the control variable is a potential and the state equation is an elliptic partial differential equation of a Schr\"odinger type, governed by the Laplace operator. The cost functional…

Optimization and Control · Mathematics 2023-02-07 Giuseppe Buttazzo , Juan Casado_Díaz , Faustino Maestre

In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…

Systems and Control · Electrical Eng. & Systems 2024-07-04 Gilberto O. Corrêa , Marlon M. López-Flores , Alexandre L. Madureira

In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…

Numerical Analysis · Mathematics 2016-08-31 Wei Gong , Ningning Yan

We consider an elliptic optimal control problem where the objective functional contains an integral along a surface of codimension 1, also known as a hypersurface. In particular, we use a fidelity term that encourages the state to take…

Numerical Analysis · Mathematics 2014-11-19 C. Brett , A. S. Dedner , C. M. Elliott

A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…

Optimization and Control · Mathematics 2017-05-03 Shinji Tanimoto

We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…

Optimization and Control · Mathematics 2017-06-09 Pablo Pedregal