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In 1980, Las Vergnas defined a notion of discrete convexity for oriented matroids, which Edelman subsequently related to the theory of anti-exchange closure functions and convex geometries. In this paper, we use generalized matroid activity…

Combinatorics · Mathematics 2021-03-30 Bryan R. Gillespie

In this paper we discuss the properties of the biordered set obtained from a complemented modular lattice and defines an operation using the sandwich elements of the biordered set. Further we describe a biordered subset satisfying certain…

Rings and Algebras · Mathematics 2020-06-04 P. G. Romeo , Akhila. R

A univariate continuous function can always be decomposed as the sum of a non-increasing function and a non-decreasing one. Based on this property, we propose a non-parametric regression method that combines two spline-fitted monotone…

Methodology · Statistics 2024-04-11 Lijun Wang , Xiaodan Fan , Hongyu Zhao , Jun S. Liu

This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a…

Optimization and Control · Mathematics 2025-07-18 Hassan Saoud , Michel Théra , Minh N. Dao

We describe a combinatorial algorithm which, given a monotone and consistent symmetric set function d on a finite set V in the sense of Rizzi, constructs a non trivial set S minimizing d(S,V-S). This includes the possibility for the…

Discrete Mathematics · Computer Science 2007-05-23 Michael Brinkmeier

The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…

Optimization and Control · Mathematics 2019-12-10 Ashkan Mohammadi , Boris S. Mordukhovich , M. Ebrahim Sarabi

A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exists points whose image under…

Numerical Analysis · Mathematics 2010-05-06 Björn S. Rüffer , Fabian R. Wirth

We propose two kinds of model order reduction methods for discrete time-delay systems with inhomogeneous initial conditions. The peculiar properties of discrete Walsh functions are directly utilized to compute the Walsh coefficients of the…

Optimization and Control · Mathematics 2024-06-07 Xiaolong Wang , Kejia Xu

A super-stable matching, which was introduced by Irving, is a solution concept in a variant of the stable matching problem in which the preferences may contain ties. Irving proposed a polynomial-time algorithm for the problem of finding a…

Computer Science and Game Theory · Computer Science 2022-06-30 Naoyuki Kamiyama

The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes of nonsmooth optimization problems. These algorithms are based on the theory and calculations of…

Optimization and Control · Mathematics 2022-01-20 Pham Duy Khanh , Boris Mordukhovich , Vo Thanh Phat , Dat Ba Tran

In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…

Data Structures and Algorithms · Computer Science 2018-03-19 Marko Mitrovic , Moran Feldman , Andreas Krause , Amin Karbasi

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid,…

Artificial Intelligence · Computer Science 2012-09-26 Lirun Su , William Zhu

In a stochastic probing problem we are given a universe $E$, where each element $e \in E$ is active independently with probability $p_e$, and only a probe of e can tell us whether it is active or not. On this universe we execute a process…

Data Structures and Algorithms · Computer Science 2014-02-19 Marek Adamczyk , Maxim Sviridenko , Justin Ward

We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…

Rings and Algebras · Mathematics 2007-12-04 Mark Kambites

We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…

Combinatorics · Mathematics 2024-04-17 Vincent Beck , Cédric Lecouvey

We consider the problem of deciding whether the solution sets of a parametrized polynomial system are toric in the sense that they admit a monomial parametrization. We focus on vertically parametrized systems, which are sparse systems where…

Algebraic Geometry · Mathematics 2026-05-15 Elisenda Feliu , Oskar Henriksson

The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…

Dynamical Systems · Mathematics 2025-11-07 Jonah Botvinick-Greenhouse , Maria Oprea , Romit Maulik , Yunan Yang

Simultaneous matrix diagonalization is used as a subroutine in many machine learning problems, including blind source separation and paramater estimation in latent variable models. Here, we extend algorithms for performing joint…

Numerical Analysis · Computer Science 2015-05-12 Volodymyr Kuleshov , Arun Tesjavi Chaganty , Percy Liang

Using the theory of Hilbert direct integrals, we introduce and study a monotonicity-preserving operation, termed the integral resolvent mixture. It combines arbitrary families of monotone operators acting on different spaces and linear…

Optimization and Control · Mathematics 2024-08-13 Minh N. Bùi , Patrick L. Combettes

Constrained submodular maximization problems have long been studied, with near-optimal results known under a variety of constraints when the submodular function is monotone. The case of non-monotone submodular maximization is less…

Data Structures and Algorithms · Computer Science 2010-10-07 Anupam Gupta , Aaron Roth , Grant Schoenebeck , Kunal Talwar