相关论文: Multiple Shape Registration using Constrained Opti…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
This paper is devoted to the analysis of multiphase shape optimization problems, which can formally be written as $\min\Big\{{g}(F_1(\Omega_1),\dots,F_h(\Omega_h))+ m\vert\,\bigcup_{i=1}^h\Omega_i\vert :\ \Omega_i\subset D,\ \Omega_i\cap…
Registration is an essential tool in image analysis. Deep learning based alternatives have recently become popular, achieving competitive performance at a faster speed. However, many contemporary techniques are limited to volumetric…
We present a fast learning-based algorithm for deformable, pairwise 3D medical image registration. Current registration methods optimize an objective function independently for each pair of images, which can be time-consuming for large…
We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie…
The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a…
Parabolic optimal control problems with control constraints are generally challenging, from either theoretical analysis or algorithmic design perspectives. Conceptually, the well-known alternating direction method of multipliers (ADMM) can…
We are interested in geometric approximation by parameterization of two-dimensional multiple-component shapes, in particular when the number of components is a priori unknown. Starting a standard method based on successive shape…
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
This paper studies the problem of distributed formation maneuver control of multi-agent systems via complex Laplacian. We will show how to change the translation, scaling, rotation, and also the shape of formation continuously by only…
In this paper, we propose two novel decentralized optimization frameworks for multi-agent nonlinear optimal control problems in robotics. The aim of this work is to suggest architectures that inherit the computational efficiency and…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
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,…
A geometric approach to time-dependent optimal control problems is proposed. This formulation is based on the Skinner and Rusk formalism for Lagrangian and Hamiltonian systems. The corresponding unified formalism developed for optimal…
This paper discusses the mathematical framework for designing methods of large deformation matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, a…
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…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
In this paper we consider an intrinsic point of view to describe the equations of motion for higher-order variational problems with constraints on higher-order trivial principal bundles. Our techniques are an adaptation of the classical…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
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…