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In this paper we consider Lipschitz graphs of functions which are stationary points of strictly polyconvex energies. Such graphs can be thought as integral currents, resp. varifolds, which are stationary for some elliptic integrands. The…

Analysis of PDEs · Mathematics 2019-10-14 Camillo De Lellis , Guido De Philippis , Bernd Kirchheim , Riccardo Tione

A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…

Numerical Analysis · Mathematics 2026-03-05 Nicholas J. E. Richardson , Noah Marusenko , Michael P. Friedlander

In this paper we focus on the convergence analysis of the forward-backward splitting method for solving nonsmooth optimization problems in Hilbert spaces when the objective function is the sum of two convex functions. Assuming that one of…

Optimization and Control · Mathematics 2016-10-17 J. Y. Bello Cruz , T. T. A. Nghia

We study linear integro-differential equations in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations are covered by the class of…

Analysis of PDEs · Mathematics 2016-04-05 Sascha Trostorff

This paper explores a family of generalized sweeping preconditionners for Helmholtz problems with non-overlapping checkerboard partition of the computational domain. The domain decomposition procedure relies on high-order transmission…

Numerical Analysis · Mathematics 2022-01-17 Ruiyang Dai , Axel Modave , Jean-François Remacle , Christophe Geuzaine

This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed…

Optimization and Control · Mathematics 2024-09-17 Zheng Zhou , Bing Tan , Songxiao Li

We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other…

Systems and Control · Electrical Eng. & Systems 2020-11-30 Zheming Wang , Raphaël M. Jungers , Chong-Jin Ong

This paper addresses a new class of generalized Bolza problems governed by nonconvex integro-differential inclusions with endpoint constraints on trajectories, where the integral terms are given in the general (with time-dependent…

Optimization and Control · Mathematics 2024-10-07 Abderrahim Bouach , Tahar Haddad , Boris S. Mordukhovich

In this article, we propose a general framework for the study of differential inclusions in the Wasserstein space of probability measures. Based on earlier geometric insights on the structure of continuity equations, we define solutions of…

Optimization and Control · Mathematics 2020-07-28 Benoît Bonnet , Hélène Frankowska

In this article we present a modified S-iteration process that we combine with inertial extrapolation to find a common solution to the split monotone inclusion problem and the fixed point problem in real Hilbert space.Our goal is to…

Numerical Analysis · Mathematics 2021-10-11 Shamshad Husain , Uqba Rafat

The paper concerns the investigation of nonconvex and nondifferentiable integral functionals on general Banach spaces, which may not be reflexive and/or separable. Considering two major subdifferentials of variational analysis, we derive…

Optimization and Control · Mathematics 2016-03-28 Boris S. Mordukhovich , Nobusumi Sagara

Rademacher theorem asserts that Lipschitz continuous functions between Euclidean spaces are differentiable almost everywhere. In this work we extend this result to set-valued maps using an adequate notion of set-valued differentiability…

Classical Analysis and ODEs · Mathematics 2022-12-14 Aris Daniilidis , Marc Quincampoix

This paper introduces the recursive sweeping preconditioner for the numerical solution of the Helmholtz equation in 3D. This is based on the earlier work of the sweeping preconditioner with the moving perfectly matched layers (PMLs). The…

Numerical Analysis · Mathematics 2015-02-26 Fei Liu , Lexing Ying

Solutions to nonlinear integro-differential systems are regular outside a negligible closed subset whose Hausdorff dimension can be explicitly bounded from above. This subset can be characterized using quantitative, universal energy…

Analysis of PDEs · Mathematics 2025-01-16 Cristiana De Filippis , Giuseppe Mingione , Simon Nowak

We develop a higher regularity theory for general quasilinear elliptic equations and systems in divergence form with random coefficients. The main result is a large-scale $L^\infty$-type estimate for the gradient of a solution. The estimate…

Analysis of PDEs · Mathematics 2016-01-27 Scott N. Armstrong , Jean-Christophe Mourrat

We establish the Lipschitz regularity of the a priori bounded local minimizers of integral functionals with non autonomous energy densities satisfying non standard growth conditions under a sharp bound on the gap between the growth and the…

Analysis of PDEs · Mathematics 2023-10-10 Michela Eleuteri , Antonia Passarelli di Napoli

In this report, we address differential systems with Lipschitz non linearities; this study is motivated by the subject of vibrations of structures with unilateral springs or non linear stress-strain law close to the linear case. We consider…

Dynamical Systems · Mathematics 2011-07-15 Bernard Rousselet

We present an existence result for a partial differential inclusion with linear parabolic principal part and relaxed one-sided Lipschitz multivalued nonlinearity in the framework of Gelfand triples. Our study uses discretizations of the…

Analysis of PDEs · Mathematics 2017-10-31 Wolf-Jürgen Beyn , Etienne Emmrich , Janosch Rieger

In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is point-wise smaller (in the sense…

Systems and Control · Computer Science 2021-07-07 Rushikesh Kamalapurkar , Warren E. Dixon , Andrew R. Teel

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

Optimization and Control · Mathematics 2011-01-10 Luis M. Briceño-Arias