English
Related papers

Related papers: An Alternate Method for Minimizing $\chi^2$

200 papers

We study the worst-case convergence rates of the proximal gradient method for minimizing the sum of a smooth strongly convex function and a non-smooth convex function whose proximal operator is available. We establish the exact worst-case…

Optimization and Control · Mathematics 2020-03-03 Adrien B. Taylor , Julien M. Hendrickx , François Glineur

This paper presents a new optimization approach for designing minimum-cost fail-safe distributions of fluid viscous dampers for seismic retrofitting. Failure is modeled as either complete damage of the dampers or partial degradation of the…

Computational Engineering, Finance, and Science · Computer Science 2020-07-16 Nicolò Pollini

In this paper, we consider two variants of the concept of sharp minimum for mathematical programming problems with quasiconvex objective function and inequality constraints. It investigated the problem of describing a variant of a simple…

Optimization and Control · Mathematics 2023-12-29 S. M. Puchinin , E. R. Korolkov , F. S. Stonyakin , M. S. Alkousa , A. A Vyguzov

Minimizing loss functions is central to machine-learning training. Although first-order methods dominate practical applications, higher-order techniques such as Newton's method can deliver greater accuracy and faster convergence, yet are…

Machine Learning · Computer Science 2025-11-25 Giuseppe Carrino , Elena Loli Piccolomini , Elisa Riccietti , Theo Mary

In second-order optimization, a potential bottleneck can be computing the Hessian matrix of the optimized function at every iteration. Randomized sketching has emerged as a powerful technique for constructing estimates of the Hessian which…

Optimization and Control · Mathematics 2021-07-16 Michał Dereziński , Jonathan Lacotte , Mert Pilanci , Michael W. Mahoney

This paper presents a finite difference quasi-Newton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing…

Optimization and Control · Mathematics 2019-01-09 Albert S. Berahas , Richard H. Byrd , Jorge Nocedal

We investigate the fundamental optimization question of minimizing a target function $f$, whose gradients are expensive to compute or have limited availability, given access to some auxiliary side function $h$ whose gradients are cheap or…

Machine Learning · Computer Science 2025-12-19 El Mahdi Chayti , Sai Praneeth Karimireddy

This paper studies the distributed minimax optimization problem over networks. To enhance convergence performance, we propose a distributed optimistic gradient tracking method, termed DOGT, which solves a surrogate function that captures…

Optimization and Control · Mathematics 2025-09-01 Yan Huang , Jinming Xu , Jiming Chen , Karl Henrik Johansson

Motivated by conforming finite element methods for elliptic problems of second order, we analyze the approximation of the gradient of a target function by continuous piecewise polynomial functions over a simplicial mesh. The main result is…

Numerical Analysis · Mathematics 2018-03-07 Andreas Veeser

We consider the global minimization of smooth functions based solely on function evaluations. Algorithms that achieve the optimal number of function evaluations for a given precision level typically rely on explicitly constructing an…

Optimization and Control · Mathematics 2020-12-23 Alessandro Rudi , Ulysse Marteau-Ferey , Francis Bach

This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…

Optimization and Control · Mathematics 2025-01-14 Raghu Bollapragada , Cem Karamanli

In this paper, we consider the minimization of a $C^2-$smooth and strongly convex objective depending on a given parameter, which is usually found in many practical applications. We suppose that we desire to solve the problem with some…

Optimization and Control · Mathematics 2025-03-14 Jean-Jacques Godeme

We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…

Optimization and Control · Mathematics 2020-11-20 Kimon Antonakopoulos , E. Veronica Belmega , Panayotis Mertikopoulos

The problem of solving partial differential equations (PDEs) can be formulated into a least-squares minimization problem, where neural networks are used to parametrize PDE solutions. A global minimizer corresponds to a neural network that…

Numerical Analysis · Mathematics 2020-12-14 Tao Luo , Haizhao Yang

We present algorithms (a) for nested neural likelihood-to-evidence ratio estimation, and (b) for simulation reuse via an inhomogeneous Poisson point process cache of parameters and corresponding simulations. Together, these algorithms…

Instrumentation and Methods for Astrophysics · Physics 2020-12-01 Benjamin Kurt Miller , Alex Cole , Gilles Louppe , Christoph Weniger

Building on previous research of Chi and Chi (2022), the current paper revisits estimation in robust structured regression under the $\text{L}_2\text{E}$ criterion. We adopt the majorization-minimization (MM) principle to design a new…

Methodology · Statistics 2023-04-25 Xiaoqian Liu , Eric C. Chi , Kenneth Lange

We consider using gradient descent to minimize the nonconvex function $f(X)=\phi(XX^{T})$ over an $n\times r$ factor matrix $X$, in which $\phi$ is an underlying smooth convex cost function defined over $n\times n$ matrices. While only a…

Optimization and Control · Mathematics 2025-04-22 Gavin Zhang , Salar Fattahi , Richard Y. Zhang

Recently, the prediction-correction method has been developed to solve nonlinear convex optimization problems. However, its convergence rate is often poor since large regularization parameters are set to ensure convergence conditions. In…

Optimization and Control · Mathematics 2024-11-05 Sai Wang

We present pyLIMASS, a novel algorithm for estimating the physical properties of the lensing system in microlensing events. The main idea of pyLIMASS is to combine all available information regarding the microlensing event, defined as…

Instrumentation and Methods for Astrophysics · Physics 2024-05-06 E. Bachelet , M. Hundertmark , S. Calchi Novati

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

Optimization and Control · Mathematics 2022-02-16 Meng Li , Paul Grigas , Alper Atamturk