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Total Generalized Variation
The novel concept of total generalized variation of a function $u$ is introduced, and some of its essential properties are proved. Differently from the bounded variation seminorm, the new concept
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
TLDR
The notion of slant differentiability is recalled and it is argued that the $\max$-function is slantly differentiable in Lp-spaces when appropriately combined with a two-norm concept, which leads to new local convergence results of the primal-dual active set strategy.
Galerkin proper orthogonal decomposition methods for parabolic problems
Summary. In this work error estimates for Galerkin proper orthogonal decomposition (POD) methods for linear and certain non-linear parabolic systems are proved. The resulting error bounds depend on
Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
TLDR
Error estimates for Galerkin proper orthogonal decomposition (POD) methods for nonlinear parabolic systems arising in fluid dynamics are proved and the backward Euler scheme is considered.
Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition
TLDR
POD is utilized to solve open-loop and closed-loop optimal control problems for the Burgers equation to comparison of POD-based algorithms with numerical results obtained from finite-element discretization of the optimality system.
Estimation Techniques for Distributed Parameter Systems
The research detailed in this monograph was originally motivated by our interest in control problems involving partial and delay differential equations. Our attempts to apply control theory
The linear regulator problem for parabolic systems
We present an approximation framework for computation (in finite dimensional spaces) of Riccati operators that can be guaranteed to converge to the Riccati operator in feedback controls for abstract
Convergence rates for Tikhonov regularisation of non-linear ill-posed problems
The authors consider non-linear ill-posed problems in a Hilbert space setting, they show that Tikhonov regularisation is a stable method for solving non-linear ill-posed problems and give conditions
Primal-Dual Strategy for Constrained Optimal Control Problems
An algorithm for efficient solution of control constrained optimal control problems is proposed and analyzed. It is based on an active set strategy involving primal as well as dual variables. For
Semi-smooth Newton methods for state-constrained optimal control problems
  • K. Ito, K. Kunisch
  • Mathematics, Computer Science
    Syst. Control. Lett.
  • 22 October 2003
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