Related papers: Shape optimisation with nearly conformal transform…

In this article we propose a scalable shape optimization algorithm which is tailored for large scale problems and geometries represented by hierarchically refined meshes. Weak scalability and grid independent convergence is achieved via a…

In this research, we investigate a general shape optimization problem in which the state equation is expressed using a nonlocal and nonlinear operator. We prove the existence of a minimum point for a functional $F$ defined on the family of…

We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D shape represented as a planar curve and a 3D shape represented as a surface; the output is a continuous curve on the surface. We cast the problem…

We develop mathematical models for shape design and topology optimization in structural contact problems involving friction between elastic and rigid bodies. The governing mechanical constraint is a nonlinear, non-smooth, and non-convex…

Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric…

Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes…

Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have…

This article presents a new and efficient alternative to well established algorithms for molecular geometry optimization. The new approach exploits the approximate decoupling of molecular energetics in a curvilinear internal coordinate…

We sketch an application of proximal algorithms to the deformation of de Rham currents into cycles, which is presented as a convex optimization problem. Emphasis is placed on the use of total variation denoising for differential forms,…

Since shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations, we show how shape optimization techniques can also be applied to an interface identification problem…

A computer-assisted proof is proposed for the Laplacian eigenvalue minimization problems over triangular domains under diameter constraints. The proof utilizes recently developed guaranteed computation methods for both eigenvalues and…

We prove and apply an optimal low-rank approximation of the Cauchy kernel over separated real domains. A skeleton decomposition is the minimum over real-valued functions of the maximum relative pointwise error. We present an algorithm to…

This paper is concerned with the minimisation of peak stresses occurring in linear elasticity. We propose to minimise the maximal von Mises stress of the elastic body. This leads to a nonsmooth shape functional. We derive the shape…

This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The problem enables us to consider Riemannian hierarchical optimization problems over complicated sets,…

We propose a new 2D shape decomposition method based on the short-cut rule. The short-cut rule originates from cognition research, and states that the human visual system prefers to partition an object into parts using the shortest possible…

Since the first optimality proofs for adaptive mesh refinement algorithms in the early 2000s, the theory of optimal mesh refinement for PDEs was inherently limited to stationary problems. The reason for this is that time-dependent problems…

We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…

New algorithms are presented for numerical conformal mapping based on rational approximations and the solution of Dirichlet problems by least-squares fitting on the boundary. The methods are targeted at regions with corners, where the…

Least squares is by far the simplest and most commonly applied computational method in many fields. In almost all applications, the least squares objective is rarely the true objective. We account for this discrepancy by parametrizing the…

We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…