Related papers: Practical Perspectives on Symplectic Accelerated O…
Time-symmetric integration schemes share with symplectic schemes the property that their energy errors show a much better behavior than is the case for generic integration schemes. Allowing adaptive time steps typically leads to a loss of…
The Euclidean space notion of convex sets (and functions) generalizes to Riemannian manifolds in a natural sense and is called geodesic convexity. Extensively studied computational problems such as convex optimization and sampling in convex…
Planning for legged-wheeled machines is typically done using trajectory optimization because of many degrees of freedom, thus rendering legged-wheeled planners prone to falling prey to bad local minima. We present a combined sampling and…
The article is aimed to address a mutually boosting use of asymptotic analysis and machine learning, for fast stiffness design of configurations infilled with smoothly-varying graded microstructures. The discussion is conducted in the…
Simulation of many-particle system evolution by molecular dynamics takes to decrease integration step to provide numerical scheme stability on the sufficiently large time interval. It leads to a significant increase of the volume of…
In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order…
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…
It can be computationally advantageous to perform computer simulations in a Lorentz boosted frame for a certain class of systems. However, even if the computer model relies on a covariant set of equations, it has been pointed out that…
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…
In this paper we develop a novel, discrete-time optimal control framework for mechanical systems with uncertain model parameters. We consider finite-horizon problems where the performance index depends on the statistical moments of the…
For real-time multirotor kinodynamic motion planning, the efficiency of sampling-based methods is usually hindered by difficult-to-sample homotopy classes like narrow passages. In this paper, we address this issue by a hybrid scheme. We…
Conic optimization plays a crucial role in many machine learning (ML) problems. However, practical algorithms for conic constrained ML problems with large datasets are often limited to specific use cases, as stochastic algorithms for…
We study novel robust zero-order algorithms with acceleration for the solution of real-time optimization problems. In particular, we propose a family of extremum seeking dynamics that can be universally modeled as singularly perturbed…
The systematization of the purely Lagrangean approach to constrained systems in the form of an algorithm involves the iterative construction of a generalized Hessian matrix W taking a rectangular form. This Hessian will exhibit as many left…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
We show that stochastic acceleration can be achieved under the perturbed iterate framework (Mania et al., 2017) in asynchronous lock-free optimization, which leads to the optimal incremental gradient complexity for finite-sum objectives. We…
As datasets continue to increase in size and multi-core computer architectures are developed, asynchronous parallel optimization algorithms become more and more essential to the field of Machine Learning. Unfortunately, conducting the…
We implement several symplectic integrators, which are based on two part splitting, for studying the chaotic behavior of one- and two-dimensional disordered Klein-Gordon lattices with many degrees of freedom and investigate their numerical…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
Tuning particle accelerators is a challenging and time-consuming task that can be automated and carried out efficiently using suitable optimization algorithms, such as model-based Bayesian optimization techniques. One of the major…