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Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…
In this paper, we study the stabilizer-free weak Galerkin methods on polytopal meshes for a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient. With certain…
We present a new method for minimizing the sum of a differentiable convex function and an $\ell_1$-norm regularizer. The main features of the new method include: $(i)$ an evolving set of indices corresponding to variables that are predicted…
An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of…
We consider an optimal shape design problem for the plate equation, where the variable thickness of the plate is the design function. This problem can be formulated as a control in the coefficient PDE-constrained optimal control problem…
This work establishes a novel, unified theoretical framework for a class of high order embedded boundary methods, revealing that the Reconstruction for Off-site Data (ROD) treatment shares a fundamental structure with the recently developed…
We present a higher order stabilization-free virtual element method applied to plane elasticity problems. We utilize a serendipity approach to reduce the total number of degrees of freedom from the corresponding high-order approximations.…
We consider single-source shortest path algorithms that perform a sequence of relaxation steps whose ordering depends only on the input graph structure and not on its weights or the results of prior steps. Each step examines one edge of the…
The anomalous rod shape in carbon isotopes has been investigated in the framework of the cranking covariant density functional theory, and two mechanisms to stabilize such a novel shape with respect to the bending motion, extreme spin, and…
In this paper, we analyze a hybridized discontinuous Galerkin(HDG) method with reduced stabilization for the Stokes equations. The reduced stabilization enables us to reduce the number of facet unknowns and improve the computational…
This paper aims to solve the equations of geometrically exact 3D nonlinear Cosserat static rods under large displacements with a mesh free alternative method to finite elements: the shooting method. One of the main goal of the work…
We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…
We present a new approach to learning the structure and parameters of a Bayesian network based on regularized estimation in an exponential family representation. Here we show that, given a fixed variable order, the optimal structure and…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
An optimal and robust low-order nonconforming finite element method is developed for the strain gradient elasticity (SGE) model in arbitrary dimension. An $H^2$-nonconforming quadratic vector-valued finite element in arbitrary dimension is…
We consider a dynamical elasto-plasticity system with Kelvin--Voigt viscosity and linear kinematic hardening of Melan--Prager type. The model is formulated in a variational framework in which a constraint set for the stress evolves in time…
We study first-order algorithms that are uniformly stable for empirical risk minimization (ERM) problems that are convex and smooth with respect to $p$-norms, $p \geq 1$. We propose a black-box reduction method that, by employing properties…
This paper deals with the development and analysis of novel time-optimal point-to-point model predictive control concepts for nonlinear systems. Recent approaches in the literature apply a time transformation, however, which do not maintain…
The same type of objects in different images may vary in their shapes because of rigid and non-rigid shape deformations, occluding foreground as well as cluttered background. The problem concerned in this work is the shape extraction in…
This work presents a novel version of recently developed Gauss-Newton method for solving systems of nonlinear equations, based on upper bound of solution residual and quadratic regularization ideas. We obtained for such method global…