相关论文: G\^ateaux semiderivative approach applied to shape…
This paper sets up an approach for shape optimization problems constrained by variational inequalities (VI) in an appropriate shape space. In contrast to classical VI, where no explicit dependence on the domain is given, VI constrained…
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…
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…
This paper is devoted to a study of time-dependent hemivariational inequality. We prove existence and uniqueness of its solution, provide fully discrete scheme and reformulate this scheme as a series of nonsmooth optimization problems. This…
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…
In this paper we introduce an abstract nonsmooth optimization problem and prove existence and uniqueness of its solution. We present a numerical scheme to approximate this solution. The theory is later applied to a sample static contact…
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…
We consider a parametric quasi-variational inequality (QVI) without any convexity assumption. Using the concept of \emph{optimal value function}, we transform the problem into that of solving a nonsmooth system of inequalities. Based on…
In this paper, we present some new necessary and sufficient optimality conditions in terms of the Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of…
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…
This thesis deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…
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 paper we present an abstract nonsmooth optimization problem for which we recall existence and uniqueness results. We show a numerical scheme to approximate its solution. The theory is later applied to a sample static contact problem…
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…
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 devoted to the theoretical and numerical study of an optimal design problem in high-temperature superconductivity (HTS). The shape optimization problem is to find an optimal superconductor shape which minimizes a certain cost…
Variational-hemivariational inequalities are an important mathematical framework for nonsmooth problems. The framework can be used to study application problems from physical sciences and engineering that involve non-smooth and even…
This work deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
Design optimization problems, e.g., shape optimization, that involve deformable bodies in unilateral contact are challenging as they require robust contact solvers, complex optimization methods that are typically gradient-based, and…