相关论文: Re-examining the Legendre-Gauss-Lobatto Pseudospec…

We consider the numerical solution of the inertial version of Landau-Lifshitz-Gilbert equation (iLLG), which describes high-frequency nutation on top of magnetization precession due to angular momentum relaxation. The iLLG equation defines…

In this paper we consider finding a second-order stationary point (SOSP) of nonconvex equality constrained optimization when a nearly feasible point is known. In particular, we first propose a new Newton-CG method for finding an approximate…

We present a direct numerical method for the solution of an optimal control problem controlling the growth of LDL, HDL and plaque. The optimal control problem is constrained with a system of coupled nonlinear free and mixed boundary partial…

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…

In this paper, we study the use of state-of-the-art nonlinear system identification techniques for the optimal control of nonlinear systems. We show that the nonlinear systems identification problem is equivalent to estimating the…

This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…

A new spectral conjugate subgradient method is presented to solve nonsmooth unconstrained optimization problems. The method combines the spectral conjugate gradient method for smooth problems with the spectral subgradient method for…

The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time variant of the well-known Differential Dynamic Programming (DDP) technique with a Gauss-Newton Hessian approximation. This family of methods has gained popularity in the…

A local convergence rate is established for an orthogonal collocation method based on Radau quadrature applied to an unconstrained optimal control problem. If the continuous problem has a sufficiently smooth solution and the Hamiltonian…

We develop a novel technique to measure small angular and lateral displacements of structured light beams. The technique relies on using high-order Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) modes, which have well-defined symmetry…

Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD)…

In this work, we analyse the discretisation of a recently proposed new Lagrangian approach to optimal control problems of affine-controlled second-order differential equations with cost functions quadratic in the controls. We propose exact…

Robot programming tools ranging from inverse kinematics (IK) to model predictive control (MPC) are most often described as constrained optimization problems. Even though there are currently many commercially-available second-order solvers,…

We propose a new method for few-shot 3D reconstruction that integrates global and local frequency regularization to stabilize geometry and preserve fine details under sparse-view conditions, addressing a key limitation of existing 3D…

This paper proposes and develops new linesearch methods with inexact gradient information for finding stationary points of nonconvex continuously differentiable functions on finite-dimensional spaces. Some abstract convergence results for a…

This paper is concerned with a linear-quadratic (LQ, for short) optimal control problem for backward stochastic differential equations (BSDEs, for short), where the coefficients of the backward control system and the weighting matrices in…

$L^1$ based optimization is widely used in image denoising, machine learning and related applications. One of the main features of such approach is that it naturally provide a sparse structure in the numerical solutions. In this paper, we…

Log-det semidefinite programming (SDP) problems are optimization problems that often arise from Gaussian graphic models. A log-det SDP problem with an l1-norm term has been examined in many methods, and the dual spectral projected gradient…

We present a comparison between finite differences schemes and a pseudospectral method applied to the numerical integration of stochastic partial differential equations that model surface growth. We have studied, in 1+1 dimensions, the…

This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value problems. While presently known techniques realize a growth of…