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Related papers: Fast B-spline Curve Fitting by L-BFGS

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L-BFGS is the state-of-the-art optimization method for many large scale inverse problems. It has a small memory footprint and achieves superlinear convergence. The method approximates Hessian based on an initial approximation and an update…

Numerical Analysis · Mathematics 2021-03-19 Hari Om Aggrawal , Jan Modersitzki

This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is…

Statistics Theory · Mathematics 2017-03-09 Qingguo Tang , Linglong Kong , David Ruppert , Rohana J. Karunamuni

We revisit the stochastic limited-memory BFGS (L-BFGS) algorithm. By proposing a new framework for the convergence analysis, we prove improved convergence rates and computational complexities of the stochastic L-BFGS algorithms compared to…

Optimization and Control · Mathematics 2018-02-14 Renbo Zhao , William B. Haskell , Vincent Y. F. Tan

In simulation technology, computationally expensive objective functions are often replaced by cheap surrogates, which can be obtained by interpolation. Full grid interpolation methods suffer from the so-called curse of dimensionality,…

Numerical Analysis · Mathematics 2019-10-15 Julian Valentin

The current over-provisioned heterogeneous multi-cores require effective run-time optimization strategies, and the run-time power monitoring subsystem is paramount for their success. Several state-of-the-art methodologies address the design…

Hardware Architecture · Computer Science 2025-01-30 Andrea Galimberti , Michele Piccoli , Davide Zoni

The estimation of functions with varying degrees of smoothness is a challenging problem in the nonparametric function estimation. In this paper, we propose the LABS (L\'{e}vy Adaptive B-Spline regression) model, an extension of the LARK…

Methodology · Statistics 2021-02-02 Sewon Park , Hee-Seok Oh , Jaeyong Lee

This paper describes an extension of the BFGS and L-BFGS methods for the minimization of a nonlinear function subject to errors. This work is motivated by applications that contain computational noise, employ low-precision arithmetic, or…

Optimization and Control · Mathematics 2021-09-10 Hao-Jun Michael Shi , Yuchen Xie , Richard Byrd , Jorge Nocedal

We propose an L-BFGS optimization algorithm on Riemannian manifolds using minibatched stochastic variance reduction techniques for fast convergence with constant step sizes, without resorting to linesearch methods designed to satisfy Wolfe…

Optimization and Control · Mathematics 2017-05-23 Anirban Roychowdhury

As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal…

Robotics · Computer Science 2023-08-29 Logan E. Beaver , Andreas A. Malikopoulos

The Finite Fourier Series (FFS) Shape-Based (SB) trajectory approximation method has been used to rapidly generate initial trajectories that satisfy the dynamics, trajectory boundary conditions, and limitation on maximum thrust…

Optimization and Control · Mathematics 2024-01-31 Caleb Gunsaulus , Carl De Vries , William Brown , Youngro Lee , Madhusudan Vijayakumar , Ossama Abdelkhalik

B\'ezier splines are widely available in various systems with the curves and surface designs. In general, the B\'ezier spline can be specified with the B\'ezier curve segments and a B\'ezier curve segment can be fitted to any number of…

Computer Vision and Pattern Recognition · Computer Science 2014-11-25 Ha Jong Won , Choe Chun Hwa , Li Kum Song

Spectral methods are renowned for their high accuracy and efficiency in solving partial differential equations. The Fourier pseudo-spectral method is limited to periodic domains and suffers from Gibbs oscillations in non-periodic problems.…

Numerical Analysis · Mathematics 2025-12-09 Dongan Li , Mou Lin , Shunxiang Cao , Shengli Chen

This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…

Computational Engineering, Finance, and Science · Computer Science 2020-06-16 Zhi Zeng , Fulei Ma

A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…

Optimization and Control · Mathematics 2018-01-22 Raino A. E. Mäkinen

We extend the well-known BFGS quasi-Newton method and its memory-limited variant LBFGS to the optimization of nonsmooth convex objectives. This is done in a rigorous fashion by generalizing three components of BFGS to subdifferentials: the…

Machine Learning · Statistics 2010-11-30 Jin Yu , S. V. N. Vishwanathan , Simon Guenter , Nicol N. Schraudolph

In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…

Optimization and Control · Mathematics 2024-06-03 Jincheng Cao , Ruichen Jiang , Erfan Yazdandoost Hamedani , Aryan Mokhtari

This article describes novel approaches to quickly estimate planar surfaces from RGBD sensor data. The approach manipulates the standard algebraic fitting equations into a form that allows many of the needed regression variables to be…

Computer Vision and Pattern Recognition · Computer Science 2021-03-12 John Papadakis , Andrew R. Willis

In this paper we describe an adaptive refinement strategy for LR B-splines. The presented strategy ensures, at each iteration, local linear independence of the obtained set of LR B-splines. This property is then exploited in two…

Numerical Analysis · Mathematics 2020-07-15 Francesco Patrizi , Carla Manni , Francesca Pelosi , Hendrik Speleers

A new efficient orthogonalization of the B-spline basis is proposed and contrasted with some previous orthogonalized methods. The resulting orthogonal basis of splines is best visualized as a net of functions rather than a sequence of them.…

Statistics Theory · Mathematics 2020-01-24 Xijia Liu , Hiba Nassar , Krzysztof PodgÓrski

In this paper we present a method for direct evaluation of generalized B-splines (GB-splines) via the local representation of these curves as piecewise functions. To accomplish this we introduce a local structure that makes GB-spline curves…

Numerical Analysis · Mathematics 2015-10-15 Ian D. Henriksen , Emily J. Evans , Derek C. Thomas