Related papers: G\^ateaux semiderivative approach applied to shape…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…
We consider vector and set optimization problems with respect to variable domination structures given by set-valued mappings acting between the preimage space and the image space of the objective mapping, as well as by set-valued mappings…
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…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
In this paper, we introduce the second-order subdifferentials for functions which are G\^ateaux differentiable on an open set and whose G\^ateaux derivative mapping is locally Lipschitz. Based on properties of this kind of second-order…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
This paper presents a novel contact-implicit trajectory optimization method using an analytically solvable contact model to enable planning of interactions with hard, soft, and slippery environments. Specifically, we propose a novel contact…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
In this chapter, we investigate recently proposed nonlinear conjugate gradient (NCG) methods for shape optimization problems. We briefly introduce the methods as well as the corresponding theoretical background and investigate their…
In this paper, we develop stochastic variance reduced algorithms for solving a class of finite-sum hemivariational inequality (HVI) problem. In this HVI problem, the associated function is assumed to be differentiable, and both the vector…
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, the shape optimization of a linear elastic body subject to frictional (Tresca) contact is investigated. Due to the projection operators involved in the formulation of the contact problem, the solution is not shape…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
This paper shows how a class of non-convex optimization problems constrained by discretized nonlinear partial differential equations may be solved to global optimality using an interior point continuation method. The solution procedure…
In this paper, we study a nonsmooth/nonconvex multiobjective optimization problem with uncertain constraints in arbitrary Asplund spaces. We first provide necessary optimality condition in a fuzzy form for approximate weakly robust…
Algorithms that solve zero-sum games, multi-objective agent objectives, or, more generally, variational inequality (VI) problems are notoriously unstable on general problems. Owing to the increasing need for solving such problems in machine…
We consider the problem of solving a smooth convex optimization problem with equality and inequality constraints in a distributed fashion. Assuming that we have a group of agents available capable of communicating over a communication…
The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…