English
Related papers

Related papers: Solving norm equations in global function fields

200 papers

Randomized zeroth-order methods are classically analyzed in expectation, but a black-box Markov conversion can give misleading high-probability guarantees, in particular by forcing the finite-difference smoothing radius to shrink with the…

Optimization and Control · Mathematics 2026-05-27 Haishan Ye

In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on two well-known projection method and the hybrid (or…

Optimization and Control · Mathematics 2015-01-30 Yu. V. Malitsky , V. V. Semenov

In this paper, we revisit the classical problem of solving over-determined systems of nonsmooth equations numerically. We suggest a nonsmooth Levenberg--Marquardt method for its solution which, in contrast to the existing literature, does…

Optimization and Control · Mathematics 2023-11-10 Lateef O. Jolaoso , Patrick Mehlitz , Alain B. Zemkoho

In this paper, we propose practical normalized stochastic first-order methods with Polyak momentum, multi-extrapolated momentum, and recursive momentum for solving unconstrained optimization problems. These methods employ dynamically…

Optimization and Control · Mathematics 2026-02-12 Chuan He , Zhaosong Lu , Defeng Sun , Zhanwang Deng

Finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian is a central problem in optimization. Regularized Newton methods are a classical tool and have been studied extensively, yet they still face…

Optimization and Control · Mathematics 2025-11-03 Yuhao Zhou , Jintao Xu , Bingrui Li , Chenglong Bao , Chao Ding , Jun Zhu

In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…

Numerical Analysis · Mathematics 2013-08-05 Erik Burman

We present our latest contributions in terms of mathematical modeling and algorithm development for the global optimization of the ACOPF problem. These contributions allow us to close the optimality gap on a number of open instances in the…

Optimization and Control · Mathematics 2020-02-21 S. Gopinath , H. L. Hijazi , T. Weisser , H. Nagarajan , M. Yetkin , K. Sundar , R. W. Bent

We study the composite convex optimization problems with a Quasi-Self-Concordant smooth component. This problem class naturally interpolates between classic Self-Concordant functions and functions with Lipschitz continuous Hessian.…

Optimization and Control · Mathematics 2023-08-29 Nikita Doikov

In this paper, we propose a smoothing method to solve nonlinear complementarity problems involving P 0-functions. We propose a nonparametric algorithm to solve the nonlinear corresponding system of equations and prove some global and local…

Optimization and Control · Mathematics 2022-02-22 El Hassene Osmani , Mounir Haddou , Lina Abdallah , Naceurdine Bensalem

Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee…

Computer Vision and Pattern Recognition · Computer Science 2016-03-02 Dylan Campbell , Lars Petersson

One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformu-lation of the problem of interest and solving the resulting problem…

Data Structures and Algorithms · Computer Science 2014-05-22 Aharon Ben-Tal , Arkadi Nemirovski

This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…

Optimization and Control · Mathematics 2024-07-23 Yao Yao , Qihang Lin , Tianbao Yang

In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…

Optimization and Control · Mathematics 2021-03-24 Nikita Doikov , Yurii Nesterov

Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…

Optimization and Control · Mathematics 2016-07-15 Vahan Hovhannisyan , Panos Parpas , Stefanos Zafeiriou

In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…

Numerical Analysis · Mathematics 2016-05-31 Kourosh Parand , Mohammad Hemami

In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…

Optimization and Control · Mathematics 2025-12-04 Matteo Lapucci , Giampaolo Liuzzi , Stefano Lucidi , Davide Pucci , Marco Sciandrone

We present two improvements to arithmetic in the Jacobian of global function fields based on the approach of Hess. The first reduces the number of expensive reduction steps by optimizing for typical inputs rather than worst-case behavior,…

Number Theory · Mathematics 2026-05-18 Vincent Macri , Michael Jacobson , Renate Scheidler

This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an…

Computational Engineering, Finance, and Science · Computer Science 2020-11-02 F. Greco , M. Arroyo

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…

Optimization and Control · Mathematics 2026-02-19 Welington de Oliveira , Johannes O. Royset

We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration…

Optimization and Control · Mathematics 2017-08-16 Dmitriy Drusvyatskiy , Courtney Paquette