Related papers: Shape optimization for variational inequalities: t…
This paper is devoted to the analysis of a second order method for recovering the \emph{a priori} unknown shape of an inclusion $\omega$ inside a body $\Omega$ from boundary measurement. This inverse problem - known as electrical impedance…
This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradients. Based on this observation, we propose three numerical…
In this paper we prove that solutions to several shape optimization problems in the plane, with a convexity constraint on the admissible domains, are polygons. The main terms of the shape functionals we consider are either E f ($\Omega$),…
This article is concerned with the reconstruction of obstacle $\O$ immersed in a fluid flowing in a bounded domain $\Omega$ in the two dimensional case. We assume that the fluid motion is governed by the Stokes-Brinkmann equations. We make…
The difference-of-convex algorithm (DCA) and its variants are the most popular methods to solve the difference-of-convex optimization problem. Each iteration of them is reduced to a convex optimization problem, which generally needs to be…
The goal of this paper is to improve the performance of an electric motor by modifying the geometry of a specific part of the iron core of its rotor. To be more precise, the objective is to smooth the rotation pattern of the rotor. A shape…
In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…
In this letter we study the proximal gradient dynamics. This recently-proposed continuous-time dynamics solves optimization problems whose cost functions are separable into a nonsmooth convex and a smooth component. First, we show that the…
In this paper we propose a novel numerical scheme for the Canham-Helfrich-Evans bending energy based on a three-field lifting procedure of the distributional shape operator to an auxiliary mean curvature field. Together with its energetic…
The present work investigates the segmentation of textures by formulating it as a strongly convex optimization problem, aiming to favor piecewise constancy of fractal features (local variance and local regularity) widely used to model…
In this paper we study an optimal shape design problem for the first eigenvalue of the fractional $p-$laplacian with mixed boundary conditions. The optimization variable is the set where the Dirichlet condition is imposed (that is…
We address the problem to infer physical material parameters and boundary conditions from the observed motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from potentially unreliable…
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…
We use a gap function in order to compare the torsional performances of different reinforced plates under the action of external forces. Then, we address a shape optimization problem, whose target is to minimize the torsional displacements…
This paper presents tractable reformulations of topology optimization problems of structures subject to frictionless unilateral contact conditions. Specifically, we consider stiffness maximization problems of trusses and continua. Based on…
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…
This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…
Fractures are normally present in the underground and are, for some physical processes, of paramount importance. Their accurate description is fundamental to obtain reliable numerical outcomes useful, e.g., for energy management. Depending…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…