Related papers: Collocation methods for second and higher order sy…
We present a new time integrator for articulated body dynamics. We formulate the governing equations of the dynamics using only the position variables and recast the position-based articulated dynamics as an optimization problem. Our…
We present high-order compact schemes for a linear second-order parabolic partial differential equation (PDE) with mixed second-order derivative terms in two spatial dimensions. The schemes are applied to option pricing PDE for a family of…
Robots often localize to lower navigational errors and facilitate downstream, high-level tasks. However, a robot may want to selectively localize when localization is costly (such as with resource-constrained robots) or inefficient (for…
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a novel first-order algorithm framework that employs a…
Imposition methods of interface conditions for the second-order wave equation with non-conforming grids is considered. The spatial discretization is based on high order finite differences with summation-by-parts properties. Previously…
A new method is described for solving optimal control problems using direct collocation at Legendre-Gauss-Lobatto points. The approach of this paper employs a polynomial approximation of the right-hand side vector field of the differential…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
In the present work, a kind of trigonometric collocation methods based on Lagrange basis polynomials is developed for effectively solving multi-frequency oscillatory second-order differential equations…
We present a systematic methodology to develop high order accurate numerical approaches for linear advection problems. These methods are based on evolving parts of the jet of the solution in time, and are thus called jet schemes. Through…
We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the P\'eclet number. In this situation, computational instabilities occur, both for steady and…
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…
In recent years, important progress has been made in applying methods and techniques of convex optimization to many fields of applications such as location science, engineering, computational statistics, and computer science. In this paper,…
Distributed optimization consists of multiple computation nodes working together to minimize a common objective function through local computation iterations and network-constrained communication steps. In the context of robotics,…
Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…
This paper addresses an optimal control problem for a robot that has to find and collect a finite number of objects and move them to a depot in minimum time. The robot has fourth-order dynamics that change instantaneously at any pick-up or…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…