Related papers: From PDEs constrained optimization to controllabil…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
This paper is concerned with the convergence rate of policy iteration for (deterministic) optimal control problems in continuous time. To overcome the problem of ill-posedness due to lack of regularity, we consider a semi-discrete scheme by…
For linear-quadratic optimal control problems (OCPs) governed by elliptic and parabolic partial differential equations (PDEs), we investigate the impact of perturbations on optimal solutions. Local perturbations may occur, e.g., due to…
Space-time finite element discretizations of time-optimal control problems governed by linear parabolic PDEs and subject to pointwise control constraints are considered. Optimal a priori error estimates are obtained for the control variable…
In this paper we investigate infinite horizon optimal control problems for parametrized partial differential equations. We are interested in feedback control via dynamic programming equations which is well-known to suffer from the curse of…
We present a pair of adjoint optimal control problems characterizing a class of time-symmetric stochastic processes defined on random time intervals. The associated PDEs are of free-boundary type. The particularity of our approach is that…
In this work we study the asymptotic behavior of the solutions of a class of abstract parabolic time optimal control problems when the generators converge, in an appropriate sense, to a given strictly negative operator. Our main application…
This paper considers the problem of designing a dynamical system to solve constrained optimization problems in a distributed way and in an anytime fashion (i.e., such that the feasible set is forward invariant). For problems with separable…
DY Gao together with some of his collaborators applied his Canonical duality theory (CDT) for solving a class of constrained optimization problems. Unfortunately, in several papers on this subject there are unclear statements, not…
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…
In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approaches and their relationship…
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…
Problem of time-optimal control of linear systems with fractional dynamics is treated in the paper from the convex-analytic standpoint. A linear system of fractional differential equations involving Riemann--Liouville derivatives is…
In this paper, we first introduce a new spatial-temporal interaction operator to describe the space-time dependent phenomena. Then we consider the stochastic optimal control of a new system governed by a stochastic partial differential…
Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such…
We propose a controllability method for the numerical solution of time-harmonic Maxwell's equations in their first-order formulation. By minimizing a quadratic cost functional, which measures the deviation from periodicity, the…
Variational formulations of time-dependent PDEs in space and time yield $(d+1)$-dimensional problems to be solved numerically. This increases the number of unknowns as well as the storage amount. On the other hand, this approach enables…
In this paper, a space-time discontinuous Galerkin finite element method for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints is studied. Time discretization is…
Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…
We propose a primal-dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling…