Related papers: Second-order Shape Optimization for Geometric Inve…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase…
We explore the use of the Gauss-Newton method for optimization in shape learning, including implicit neural surfaces and geometry-informed neural networks. The method addresses key challenges in shape learning, such as the ill-conditioning…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
Shape optimization based on the shape calculus is numerically mostly performed by means of steepest descent methods. This paper provides a novel framework to analyze shape-Newton optimization methods by exploiting a Riemannian perspective.…
We introduce a novel family of invariant, convex, and non-quadratic functionals that we employ to derive regularized solutions of ill-posed linear inverse imaging problems. The proposed regularizers involve the Schatten norms of the Hessian…
In this paper, we propose a first second-order scheme based on arbitrary non-Euclidean norms, incorporated by Bregman distances. They are introduced directly in the Newton iterate with regularization parameter proportional to the square…
In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…
We embark in a program of studying the problem of better approximating surfaces by triangulations(triangular meshes) by considering the approximating triangulations as finite metric spaces and the target smooth surface as their…
We further research on the accelerated optimization phenomenon on Riemannian manifolds by introducing accelerated global first-order methods for the optimization of $L$-smooth and geodesically convex (g-convex) or $\mu$-strongly g-convex…
The differential-geometric structure of the manifold of smooth shapes is applied to the theory of shape optimization problems. In particular, a Riemannian shape gradient with respect to the first Sobolev metric and the Steklov-Poincar\'{e}…
A class of second-order algorithms is proposed for minimizing smooth nonconvex functions that alternates between regularized Newton and negative curvature steps in an iteration-dependent subspace. In most cases, the Hessian matrix is…
This paper is devoted to the understanding of regularisation process in the shape optimization approach to the so-called Dirichlet inverse obstacle problem for elliptic operators. More precisely, we study two different regularisations of…
In this paper, we propose a new variational model for image reconstruction by minimizing the $L^1$ norm of the \emph{Weingarten map} of image surface $(x,y,f(x,y))$ for a given image $f:{\mathrm{\Omega}}\rightarrow \mathbb R$. We…
We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse…
The alternating direction method of multipliers within a shape optimization framework is developed for solving geometric inverse problems, focusing on a cavity identification problem from the perspective of non-destructive testing and…
In this paper, we are interested in shape optimization problems involving the ge ometry (normal, curvatures) of the surfaces. We consider a class of hypersurface s in $\mathbb{R}^{n}$ satisfying a uniform ball condition and we prove the…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing…