Related papers: Shape optimization for variational inequalities: t…
We propose a new conceptual approach to reach unattained dissipative properties based on the friction of slender concentric sliding columns. We begin by searching for the optimal topology in the simplest telescopic system of two concentric…
This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality.…
The problem of optimization of a cycle of tangential deformations of the surface of a spherical object (microsquirmer) self-propelling in a viscous fluid at low Reynolds numbers is represented in a noncanonical Hamiltonian form. The…
Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…
An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
The thin obstacle problem or $n$-dimensional Signorini problem is a classical variational problem arising in several applications, starting with its first introduction in elasticity theory. The vast literature concerns mostly quadratic…
This paper concerns an optimization algorithm for unconstrained non-convex problems where the objective function has sparse connections between the unknowns. The algorithm is based on applying a dissipation preserving numerical integrator,…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
Our concern is the computation of optimal shapes in problems involving $\(-\Delta)^{1/2}$. We focus on the energy $J(\Omega)$ associated to the solution $u\_\Omega$ of the basic Dirichlet problem $(-\Delta)^{1/2} u\_\Omega = 1$ in $\Omega$,…
The alternating direction method of multipliers within a shape optimization framework is developed for solving geometric inverse problems, focusing on a cavity identification problem from the perspective of non-destructive testing and…
Motivated by extrusion problems, we consider a non-stationary incompress-ible 3D fluid flow with a non-constant (temperature dependent) viscosity, subjected to mixed boundary conditions with a given time dependent velocity on a part of the…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…
Controlling the shapes of surfaces provides a novel way to direct self-assembly of colloidal particles on those surfaces and may be useful for material design. This motivates the investigation of an optimal control problem for surface shape…
We propose an adaptive optimization algorithm for solving unconstrained scaled gradient flow problems that achieves fast convergence by controlling the optimization trajectory shape and the discretization step sizes. Under a broad class of…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
With the increasing demand for the accuracy of numerical simulation of pavement mechanics, the variational inequality model and its induced finite element method which can simulate the interlayer contact state becomes a potential solution.…
We present a cut finite element method for shape optimization in the case of linear elasticity. The elastic domain is defined by a level-set function, and the evolution of the domain is obtained by moving the level-set along a velocity…
In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the standard four dimensional half sphere. We provide an Euler-Hopf type criterion for a given function to be a scalar curvature…