In this paper one and two target optimal controls of a linear diffusion equation are considered. These problems can be formulated as nonlinear, PDE-constrained optimization problems in infinite dimension. We consider two formulations, one having an inequality constraint mandating the primary target to be satisfied within a given tolerance 2, and the other having weighted norms in the cost funct...

In this paper, by using scalar multiple integral cost functionals and the notion of convexity associated with a functional driven an uncertain multi-time controlled second-order Lagrangian, we develop new mathematical framework on multi-dimensional variational control problems mixed constraints implying partial differential equations (PDEs) inequations (PDIs). Concretely, introduce investigate ...

Abstract Inverse wave problems (IWPs) amount in non-linear optimization where a certain distance between state variable and some observations of wavefield is to be minimized. Additionally, we require the solution model equation that involves set parameters optimized. Typical approaches solve IWPs includes adjoint method , which generates sequence strictly enforces at each iteration, and, recons...

we establish a relationship between general constrained pseudoconvex optimization problems and globally projected dynamical systems. a corresponding novel neural network model, which is globally convergent and stable in the sense of lyapunov, is proposed. both theoretical and numerical approaches are considered. numerical simulations for three constrained nonlinear optimization problems a...

A recently proposed trust-region approach for bound-constrained nonlinear equations is applied to the KKT systems arising from the discretization of a class of PDE-constrained optimization problems. Two different implementations are developed that take into account the large dimension and the special structure of the problems. The linear algebra phase is analyzed considering the possibility of ...

Combining the numerical concept of variational discretization introduced in [11, 12] and semi-smooth Newton methods for the numerical solution of pde constrained optimization with control constraints [9, 22] we place special emphasis on the implementation and globalization of the numerical algorithm. We prove fast local convergence of a globalized algorithm and illustrate our analytical and alg...

Standard Krylov subspace methods only allow the user to choose a single preconditioner, although in many situations there may be a number of possibilities. Here we describe an extension of GMRES, multi-preconditioned GMRES, which allows the use of more than one preconditioner. We give some theoretical results, propose a practical algorithm, and present numerical results from problems in domain ...

We consider PDE constrained shape optimization in the framework of finite element discretization of the underlying boundary value problem. Our approach employs (i) B-spline based representations of the deformation diffeomorphism, and (ii) superconvergent domain integral expressions for the shape gradient. We study the balance of the discretization errors of the finite element method and the B-s...