Related papers: Shape optimization in the space of piecewise-smoot…
Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequality constraint, which makes it challenging to derive…
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 this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
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…
Computational design optimization in fluid dynamics usually requires to solve non-linear partial differential equations numerically. In this work, we explore a Bayesian optimization approach to minimize an object's drag coefficient in…
The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…
A class of non-smooth and non-convex optimization problems with penalty constraints linked to variational inequalities (VI) is studied with respect to its shape differentiability. The specific problem stemming from quasi-brittle fracture…
This paper is concerned with a numerical simulation of shape optimization in a two-dimensional viscous incompressible flow governed by Navier--Stokes equations with mixed boundary conditions containing the pressure. The minimization problem…
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve…
Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…
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 article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
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}…
In this work, we develop a framework based on piecewize B\'ezier curves to plane shapes deformation and we apply it to shape optimization problems. We describe a general setting and some general result to reduce the study of a shape…
We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the physics. We connect the differential geometry of product shape…
This article deals with a particular class of shape and topology optimization problems: the optimized design is a region $G$ of the boundary $\partial \Omega$ of a given domain $\Omega$, which supports a particular type of boundary…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…