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Related papers: Monotone comparative statics for submodular functi…

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The theory of Monotone Comparative Statics (MCS) has traditionally required a lattice structure, excluding certain multidimensional environments such as mixed-strategy games where this property fails. We show that this structure is not…

Theoretical Economics · Economics 2026-03-06 Yeon-Koo Che , Jinwoo Kim , Fuhito Kojima

Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining…

Classical Analysis and ODEs · Mathematics 2026-04-14 Alexander Belton , Dominique Guillot , Apoorva Khare , Mihai Putinar

We study a natural generalization of stable matching to the maximum weight stable matching problem and we obtain a combinatorial polynomial time algorithm for it by reducing it to the problem of finding a maximum weight ideal cut in a DAG.…

Data Structures and Algorithms · Computer Science 2018-04-04 Tung Mai , Vijay V. Vazirani

Constrained submodular maximization has been extensively studied in the recent years. In this paper, we study adaptive robust optimization with nearly submodular structure (ARONSS). Our objective is to randomly select a subset of items that…

Machine Learning · Computer Science 2019-07-30 Shaojie Tang , Jing Yuan

The equilibrium properties of hard rod monolayers are investigated in a lattice model (where position and orientation of a rod are restricted to discrete values) as well as in an off--lattice model featuring spherocylinders with continuous…

Soft Condensed Matter · Physics 2016-09-21 M. Oettel , M. Klopotek , M. Dixit , E. Empting , T. Schilling , H. Hansen--Goos

In this work, we study the classical problem of maximizing a submodular function subject to a matroid constraint. We develop deterministic algorithms that are very parsimonious with respect to querying the submodular function, for both the…

Data Structures and Algorithms · Computer Science 2024-08-29 Eric Balkanski , Steven DiSilvio , Alan Kuhnle , ChunLi Peng

We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special…

Numerical Analysis · Mathematics 2007-05-23 Abdenasser Benahmed

The theory of monotone operators plays a major role in modern optimization and many areas of nonlinera analysis. The central classes of monotone operators are matrices with a positive semidefinite symmetric part and subsifferential…

Functional Analysis · Mathematics 2024-05-24 Salihah Thabet Alwadani

The exponential ordering is exploited in the context of non-auto\-no\-mous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as…

Dynamical Systems · Mathematics 2022-12-09 Sylvia Novo , Rafael Obaya , Ana M. Sanz , Victor M. Villarragut

Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…

Neural and Evolutionary Computing · Computer Science 2026-04-17 Liam Wigney , Frank Neumann

The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…

Combinatorics · Mathematics 2022-09-15 Vladimir Danilov

Maximizing a submodular function is a fundamental task in machine learning and in this paper we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary of the…

Data Structures and Algorithms · Computer Science 2025-05-26 Paul Dütting , Federico Fusco , Silvio Lattanzi , Ashkan Norouzi-Fard , Morteza Zadimoghaddam

Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…

Machine Learning · Computer Science 2016-02-24 Francis Bach

A matroid has been one of the most important combinatorial structures since it was introduced by Whitney as an abstraction of linear independence. As an important property of a matroid, it can be characterized by several different (but…

Combinatorics · Mathematics 2020-09-02 Takanori Maehara , So Nakashima

Submodular maximization over a matroid constraint is a fundamental problem with various applications in machine learning. Some of these applications involve decision-making over datapoints with sensitive attributes such as gender or race.…

Machine Learning · Computer Science 2023-12-25 Marwa El Halabi , Jakub Tarnawski , Ashkan Norouzi-Fard , Thuy-Duong Vuong

This paper develops algorithms to solve strong-substitutes product-mix auctions. That is, it finds competitive equilibrium prices and quantities for agents who use this auction's bidding language to truthfully express their…

Computer Science and Game Theory · Computer Science 2023-07-11 Elizabeth Baldwin , Paul W. Goldberg , Paul Klemperer , Edwin Lock

The study of matroid products traces back to the 1970s, when Lov\'asz and Mason studied the existence of various types of matroid products with different strengths. Among these, the tensor product is arguably the most important, which can…

The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this…

Data Structures and Algorithms · Computer Science 2023-05-26 Silvio Lattanzi , Slobodan Mitrović , Ashkan Norouzi-Fard , Jakub Tarnawski , Morteza Zadimoghaddam

Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…

Data Structures and Algorithms · Computer Science 2011-11-08 Shaddin Dughmi

The classical comparison-based sorting problem asks us to find the underlying total order of a given set of elements, where we can only access the elements via comparisons. In this paper, we study a restricted version, where, as a hint, a…

Data Structures and Algorithms · Computer Science 2025-07-21 Benjamin Aram Berendsohn