Related papers: A constrained shape optimization problem in Orlicz…
We prove some regularity results for a connected set S in the planar domain O, which minimizes the compliance of its complement O\S, plus its length. This problem, interpreted as to find the best location for attaching a membrane subject to…
We study an area minimization problem for spacelike zero mean curvature surfaces in four dimensional Lorentz-Minkowski space. The areas of these surfaces are compared of with the areas of certain marginally trapped surfaces having the same…
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…
In this paper we study the asymptotic behavior of some optimal design problems related to nonlinear Steklov eigenvalues, under irregular (but diffeomorphic) perturbations of the domain.
A Bernoulli free boundary problem with geometrical constraints is studied. The domain $\Om$ is constrained to lie in the half space determined by $x_1\geq 0$ and its boundary to contain a segment of the hyperplane $\{x_1=0\}$ where…
We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We…
We introduce a new optimization problem regarding embeddings of a graph into a Euclidean space and discuss its relation to the two, mutually dual, optimizations problems introduced by Goering-Helmberg-Wappler. We prove that the Laplace…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
We consider the variational problem of minimizing an anisotropic perimeter functional under a volume constraint in a Euclidean convex domain. We extend to this setting analytical properties of the isoperimetric profile, topological features…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
In this paper, we study stochastic constrained minimax optimization problems with nonconvex-nonconcave structure, a central problem in modern machine learning, for which reliable and efficient algorithms remain largely unexplored due to its…
We consider a shape optimization problem related to the persistence threshold for a biological species, the unknown shape corresponding to the zone of the habitat which is favorable to the population. Analytically, this translates in the…
We consider the shape optimization problem which consists in placing a given mass $m$ of elastic material in a design region so that the compliance is minimal. Having in mind optimal light structures, our purpose is to show that the problem…
We study the non-compact Sobolev embeddings into the optimal scale of Lorentz spaces, $W_0^mL^{p,q}(\Omega) \to L^{\frac{dp}{d - mp},r}(\Omega)$, where $\Omega \subseteq \mathbb{R}^d$, $1 \le m \le d$ and $0<q<r\le\infty$ with $1<p<\frac…
We present first a brief review of the existing literature on shape optimization, stressing the recent use of Hamiltonian systems in topology optimization. In the second section, we collect some preliminaries on the implicit parametrization…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
Spaces where each element describes a shape, so-called shape spaces, are of particular interest in shape optimization and its applications. Theory and algorithms in shape optimization are often based on techniques from differential…
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…
This paper settles the existence question for a rather general class of convex optimal design problems with a volume constraint. In low dimensions, we prove the existence of an optimal configuration for general convex minimization problems…
Wide variety of engineering design tasks can be formulated as constrained optimization problems where the shape and topology of the domain are optimized to reduce costs while satisfying certain constraints. Several mathematical approaches…