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We consider stochastic and deterministic three-wave semi-linear systems with bounded and almost continuous set of frequencies. Such systems can be obtained by considering nonlinear lattice dynamics or truncated partial differential…

Analysis of PDEs · Mathematics 2020-04-22 Erwan Faou

In this paper, the convergence of alternating minimization is established for non-smooth convex optimization in Banach spaces, and novel rates of convergence are provided. As objective function a composition of a smooth and a non-smooth…

Optimization and Control · Mathematics 2021-05-31 Jakub Wiktor Both

Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…

Optimization and Control · Mathematics 2016-04-05 Patrick Holmes , Shreyas Kousik , Shankar Mohan , Ram Vasudevan

By applying some techniques of set-valued and variational analysis, we study solution stability of nonhomogeneous split equality problems and nonhomogeneous split feasibility problems, where the constraint sets need not be convex. Necessary…

Optimization and Control · Mathematics 2024-11-19 Vu Thi Huong , Hong-Kun Xu , Nguyen Dong Yen

We develop a semismooth Newton framework for the numerical solution of fixed-point equations that are posed in Banach spaces. The framework is motivated by applications in the field of obstacle-type quasi-variational inequalities and…

Numerical Analysis · Mathematics 2024-10-01 Amal Alphonse , Constantin Christof , Michael Hintermüller , Ioannis P. A. Papadopoulos

We provide convex necessary and sufficient conditions for the robust stability of linear positively dominated systems. In particular we show that the structured singular value is always equal to its convex upper bound for nonnegative…

Optimization and Control · Mathematics 2015-08-21 Marcello Colombino , Roy S. Smith

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

Analysis of PDEs · Mathematics 2026-05-18 Minghui Bi , Yixian Gao

In the present paper, a systematic study is made of quantitative semicontinuity (a.k.a. Lipschitzian) properties of certain multifunctions, which are defined as a solution map associated to a family of parameterized ``split" feasibility…

Optimization and Control · Mathematics 2026-04-01 Amos Uderzo

The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell…

Numerical Analysis · Mathematics 2014-09-04 Jonathan Briskman , Deanna Needell

Bundle methods have been intensively studied for solving both convex and nonconvex optimization problems. In most of the bundle methods developed thus far, at least one quadratic programming (QP) subproblem needs to be solved in each…

Optimization and Control · Mathematics 2015-07-08 Shuai Liu , Andrew Eberhard , Yousong Luo

This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…

Dynamical Systems · Mathematics 2022-06-16 Mark A. Pinsky

This paper studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parametrization, the problem of finding the…

Optimization and Control · Mathematics 2019-11-26 Masaki Ogura , Masako Kishida , James Lam

We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities…

Optimization and Control · Mathematics 2020-06-02 Xiao Liu , Simge Kucukyavuz

Variational inequality problems allow for capturing an expansive class of problems, including convex optimization problems, convex Nash games and economic equilibrium problems, amongst others. Yet in most practical settings, such problems…

Optimization and Control · Mathematics 2017-02-17 Uma V. Ravat , Uday V. Shanbhag

We develop an operator-theoretic framework for stability and statistical concentration in nonlinear inverse problems with block-structured parameters. Under a unified set of assumptions combining blockwise Lipschitz geometry, local…

Computer Vision and Pattern Recognition · Computer Science 2026-02-11 Joe-Mei Feng , Hsin-Hsiung Kao

Deciding feasibility of large systems of linear equations and inequalities is one of the most fundamental algorithmic tasks. However, due to data inaccuracies or modeling errors, in practical applications one often faces linear systems that…

Data Structures and Algorithms · Computer Science 2022-09-07 Kristóf Bérczi , Alexander Göke , Lydia Mirabel Mendoza-Cadena , Matthias Mnich

This paper introduces new parameterizations of equilibrium neural networks, i.e. networks defined by implicit equations. This model class includes standard multilayer and residual networks as special cases. The new parameterization admits a…

Machine Learning · Computer Science 2020-10-06 Max Revay , Ruigang Wang , Ian R. Manchester

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

Motivated by applications requiring sparse or nonnegative controls, we investigate reachability properties of linear infinite-dimensional control problems under conic constraints. Relaxing the problem to convex constraints if the initial…

Optimization and Control · Mathematics 2024-05-14 Camille Pouchol , Emmanuel Trélat , Christophe Zhang

The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…

Dynamical Systems · Mathematics 2026-03-23 Davi Lima , Rafael Lucena