Related papers: A Joint Tikhonov Regularization and Augmented Lagr…
We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…
This two-part study is devoted to the analysis of the so-called exact augmented Lagrangians, introduced by Di Pillo and Grippo for finite dimensional optimization problems, in the case of optimization problems in Hilbert spaces. In the…
We consider time discretization methods for abstract parabolic problems with inhomogeneous linear constraints. Prototype examples that fit into the general framework are the heat equation with inhomogeneous (time dependent) Dirichlet…
A class of infinite horizon optimal control problems involving mixed quasi-norms of $L^p$-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
In this article, we consider a stochastic linear quadratic control problem with partial observation. A near optimal control in the weak formulation is characterized. The main features of this paper are the presence of the control in the…
By parametrizing input and state trajectories with basis functions different approximations to the constrained linear quadratic regulator problem are obtained. These notes present and discuss technical results that are intended to…
Minimization problems in $\ell^2$ for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted $\ell^1$ penalty term. The necessary and sufficient condition for optimality is shown to…
We systematically investigated the limited inverse discrete Fourier transform of the quasi distributions from the perspective of inverse problem theory. This transformation satisfies two of Hadamard's well-posedness criteria, existence and…
We propose a novel Galerkin discretization scheme for stochastic optimal control problems on an indefinite time horizon. The control problems are linear-quadratic in the controls, but possibly nonlinear in the state variables, and the…
In $\ell^1$-regularization, which is an important tool in signal and image processing, one usually is concerned with signals and images having a sparse representation in some suitable basis, e.g. in a wavelet basis. Many results on…
We consider the ill-posed operator equation $Ax=y$ with an injective and bounded linear operator $A$ mapping between $\ell^2$ and a Hilbert space $Y$, possessing the unique solution \linebreak $x^\dag=\{x^\dag_k\}_{k=1}^\infty$. For the…
We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously…
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the…
This paper investigates using the conjugate gradient iterative solver for ill-posed problems. We show that preconditioner and Tikhonov-regularization work in conjunction. In particular when they employ the same symmetric positive…
We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a…
Sparse training reduces the memory and computational costs of deep neural networks. However, sparse optimization methods, e.g., those adding an $\ell_1$ penalty, often control sparsity only indirectly through a regularization parameter…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
This paper is dedicated to the stability analysis of the optimal solutions of a control problem associated with a semilinear elliptic equation. The linear differential operator of the equation is neither monotone nor coercive due to the…