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Related papers: A primal approach to the Clarke-Ledyaev inequality

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In this article, we give a complex-geometric proof of the Alexandrov-Fenchel inequality without using toric compactifications. The idea is to use the Legendre transform and develop the Brascamp-Lieb proof of the Pr\'ekopa theorem. New…

Complex Variables · Mathematics 2018-02-13 Xu Wang

In this article we develop a new primal dual variational formulation suitable for a large class of non-convex problems in the calculus of variations. The results are obtained through basic tools of convex analysis, duality theory, the…

Optimization and Control · Mathematics 2019-09-05 Fabio Botelho

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…

Optimization and Control · Mathematics 2015-03-04 Quoc Tran-Dinh , Volkan Cevher

This article develops a primal dual formulation for a primal proximal approach suitable for a large class of non-convex models in the calculus of variations. The results are established through standard tools of functional analysis, convex…

Optimization and Control · Mathematics 2021-07-27 Fabio Silva Botelho

We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence…

Optimization and Control · Mathematics 2020-03-26 D. Russell Luke , Yura Malitsky

We present a short proof of the central limit theorem which is elementary in the sense that no knowledge of characteristic functions, linear operators, or other advanced results are needed. Our proof is based on Lindeberg's trick of…

Probability · Mathematics 2021-06-03 Calvin Wooyoung Chin

We prove the Levin-Ste\v{c}kin inequality using Chebyshev's inequality and symmetrization. Symmetry and slightly modified Chebyshev's inequality are also the key to an elementary proof of Clausing's inequality .

Classical Analysis and ODEs · Mathematics 2016-12-19 Alfred Witkowski

Employing the ideas of non-linear preconditioning and testing of the classical proximal point method, we formalise common arguments in convergence rate and convergence proofs of optimisation methods to the verification of a simple…

Optimization and Control · Mathematics 2020-10-06 Tuomo Valkonen

We prove that in the Ryabov paper an application of the geometric Kharlamov method to the Goryachev system yields noncommutative "new variables of separation" instead of the standard canonical variables of separation.

Exactly Solvable and Integrable Systems · Physics 2011-10-14 A. V. Tsiganov

Comparison principles are developed for discrete quasilinear elliptic partial differential equations. We consider the analysis of a class of nonmonotone Leray-Lions problems featuring both nonlinear solution and gradient dependence in the…

Numerical Analysis · Mathematics 2017-11-02 Sara Pollock , Yunrong Zhu

Recent advancements in data science have significantly elevated the importance of orthogonally constrained optimization problems. The Riemannian approach has become a popular technique for addressing these problems due to the advantageous…

Optimization and Control · Mathematics 2026-04-07 Linglingzhi Zhu , Wentao Ding , Shangyuan Liu , Anthony Man-Cho So

We prove the existence of primitive sets (sets of integers in which no element divides another) in which the gap between any two consecutive terms is substantially smaller than the best known upper bound for the gaps in the sequence of…

Number Theory · Mathematics 2019-02-06 Nathan McNew

We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…

Optimization and Control · Mathematics 2023-06-21 Jong Gwang Kim

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls…

Popular Physics · Physics 2009-11-13 J. -P. Provost , C. Bracco

This article develops a duality principle applicable to a large class of variational problems. Firstly, we apply the results to a Ginzburg-Landau type model. In a second step, we develop another duality principle and related primal dual…

Optimization and Control · Mathematics 2018-01-18 Fabio Botelho

An elementary proof of Kepler's first law, i.e. that bounded planetary orbits are elliptical, is derived without the use of calculus. The proof is similar in spirit to previous derivations, in that conservation laws are used to obtain an…

Classical Physics · Physics 2021-11-17 Akarsh Simha

In this article, we develop duality principles applicable to primal variational formulations found in the non-linear elasticity theory. As a first application, we establish the concerning results in details for one and three-dimensional…

Optimization and Control · Mathematics 2019-10-04 Fabio Botelho

We exhibit a classical model free from any paradox which exactly simulates the spin EPR test. We conclude that Bell's inequality violation is a strictly classical phenomenon, contrary to a general belief.

Quantum Physics · Physics 2008-12-26 Michel Feldmann

In this paper, a new variant of accelerated gradient descent is proposed. The pro-posed method does not require any information about the objective function, usesexact line search for the practical accelerations of convergence, converges…

Optimization and Control · Mathematics 2019-05-14 Yurii Nesterov , Alexander Gasnikov , Sergey Guminov , Pavel Dvurechensky

We investigate the computational problem of determining whether a bivariate polynomial with non-negative coefficients and no constant term can attain a prime value. While classical conjectures such as Bouniakowsky's provide necessary…

Number Theory · Mathematics 2025-05-27 K. Lakshmanan
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