Related papers: Numerical shape optimization among convex sets
A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.
Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…
Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization as optimization on Riemannian shape manifolds. We consider…
In this paper, we focus on the following general shape optimization problem: $$ \min\{J(\Om), \Om convex, \Om\in\mathcal S_{ad}\}, $$ where $\mathcal S_{ad}$ is a set of 2-dimensional admissible shapes and $J:\mathcal{S}_{ad}\to\R$ is a…
We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes…
We present SCOPE, a fast and efficient framework for modeling and manipulating deformable linear objects (DLOs). Unlike conventional energy-based approaches, SCOPE leverages convex approximations to significantly reduce computational cost…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requirements than standard body-fitted formulations. These schemes do…
Making the gradients small is a fundamental optimization problem that has eluded unifying and simple convergence arguments in first-order optimization, so far primarily reserved for other convergence criteria, such as reducing the…
In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…
This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…
We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and…
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…
Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…
We discuss a general technique that can be used to form a differentiable bound on the optima of non-differentiable or discrete objective functions. We form a unified description of these methods and consider under which circumstances the…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…