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We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a…

Optimization and Control · Mathematics 2012-05-25 Sebastian U. Stich , Christian L. Müller , Bernd Gärtner

We study the nonlinear fractional reaction diffusion equation $\partial_{t}u + (-\Delta)^{s} u= f(t,x,u)$, $s\in(0,1)$ in a bounded domain $\Omega$ together with Dirichlet boundary conditions on $\R^N \setminus \Omega$. We prove asymptotic…

Analysis of PDEs · Mathematics 2013-08-26 Sven Jarohs , Tobias Weth

This paper studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works for both undirected and directed…

Optimization and Control · Mathematics 2015-03-20 Bahman Gharesifard , Jorge Cortes

In this article we derive a strong version of the Pontryagin Maximum Principle for general nonlinear optimal control problems on time scales in finite dimension. The final time can be fixed or not, and in the case of general boundary…

Optimization and Control · Mathematics 2013-02-15 Loïc Bourdin , Emmanuel Trélat

We study the accuracy of analytical wave function based many-body methods derived by energy minimization of a Jastrow-Feenberg ansatz for electrons (`Fermi hypernetted chain / Euler Lagrange' approach). Approximations to avoid the…

Other Condensed Matter · Physics 2019-06-05 Martin Panholzer , Raphael Hobbiger , Helga Böhm

We study the discrete constrained saddle dynamics and their momentum variants for locating saddle points on manifolds. Under the assumption of exact unstable eigenvectors, we establish a local linear convergence of the discrete constrained…

Numerical Analysis · Mathematics 2026-02-02 Qiang Du , Baoming Shi

We present theoretical results on the convergence of \emph{non-convex} accelerated gradient descent in matrix factorization models with $\ell_2$-norm loss. The purpose of this work is to study the effects of acceleration in non-convex…

Machine Learning · Computer Science 2019-09-24 Tayo Ajayi , David Mildebrath , Anastasios Kyrillidis , Shashanka Ubaru , Georgios Kollias , Kristofer Bouchard

In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…

Dynamical Systems · Mathematics 2020-08-07 Mondher Benjemaa , Wided Gouadri , Mohamed Ali Hammami

Minimization methods that search along a curvilinear path composed of a non-ascent nega- tive curvature direction in addition to the direction of steepest descent, dating back to the late 1970s, have been an effective approach to finding a…

Optimization and Control · Mathematics 2017-06-06 Donald Goldfarb , Cun Mu , John Wright , Chaoxu Zhou

We investigate the stability of the equilibrium-induced optimal value in one-dimensional diffusion setting for a time-inconsistent stopping problem under non-exponential discounting. We show that the optimal value is semi-continuous with…

Probability · Mathematics 2022-10-04 Erhan Bayraktar , Zhenhua Wang , Zhou Zhou

We study solution discovery, where the goal is to obtain a feasible solution to a problem from an initial configuration by a bounded sequence of local moves. In many applications, however, the graph that defines which vertex sets are…

Quantum gases with short-range attractive interaction have a tendency to form pairs. For time-dependent interaction we find that the pairing amplitude at small separation satisfies a fractional differential equation (FDE). We derive…

Quantum Gases · Physics 2026-05-28 Uri Sharell , Tilman Enss

In this paper, we study convergence of coupled dynamical systems on convergent sequences of graphs to a continuum limit. We show that the solutions of the initial value problem for the dynamical system on a convergent graph sequence tend to…

Dynamical Systems · Mathematics 2022-05-31 Georgi S. Medvedev

The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality without any smallness assumptions on the gap between growth and coercitivity…

Analysis of PDEs · Mathematics 2020-10-09 Michela Eleuteri , Antonia Passarelli di Napoli

We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in [9],…

Analysis of PDEs · Mathematics 2021-04-05 Mauro Bonafini , Van Phu Cuong Le , Matteo Novaga , Giandomenico Orlandi

We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…

Numerical Analysis · Mathematics 2024-04-05 Antonín Češík , Sebastian Schwarzacher

We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the…

Numerical Analysis · Mathematics 2015-06-12 Hayden Schaeffer , Stanley Osher , Russel Caflisch , Cory Hauck

We study the problem of minimizing a $m$-weakly convex and possibly nonsmooth function. Weak convexity provides a broad framework that subsumes convex, smooth, and many composite nonconvex functions. In this work, we propose a…

Optimization and Control · Mathematics 2025-09-04 Feng-Yi Liao , Yang Zheng

We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that…

Statistical Mechanics · Physics 2026-01-26 Hyun-Myung Chun , Euijoon Kwon , Hyunggyu Park , Jae Sung Lee

Optimizing the energy efficiency of driving processes provides valuable insights into the underlying physics and is of crucial importance for numerous applications, from biological processes to the design of machines and robots. Knowledge…

Soft Condensed Matter · Physics 2024-04-02 Sarah A. M. Loos , Samuel Monter , Felix Ginot , Clemens Bechinger
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