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We present an optimal, combinatorial 1-1/e approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pal and Vondrak, 2008), our algorithm is…

Data Structures and Algorithms · Computer Science 2013-11-20 Yuval Filmus , Justin Ward

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

We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…

Optimization and Control · Mathematics 2024-02-14 Alberto De Marchi

We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…

Optimization and Control · Mathematics 2019-07-15 Guoyong Gu , Junfeng Yang

As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical…

Neural and Evolutionary Computing · Computer Science 2022-11-29 Chao Qian

Submodular optimization has numerous applications such as crowdsourcing and viral marketing. In this paper, we study the fundamental problem of non-negative submodular function maximization subject to a $k$-system constraint, which…

Data Structures and Algorithms · Computer Science 2021-06-16 Kai Han , Shuang Cui , Tianshuai Zhu , Jing Tang , Benwei Wu , He Huang

In contrast to the many continuous global optimization methods that assume the objective function and constraints are factorable, we study how to find globally maximal solutions to problems that are not factorable, focusing on a particular…

Optimization and Control · Mathematics 2022-08-31 Hugh Medal , Izuwa Ahanor

We connect high-dimensional subset selection and submodular maximization. Our results extend the work of Das and Kempe (2011) from the setting of linear regression to arbitrary objective functions. For greedy feature selection, this…

Machine Learning · Statistics 2017-10-13 Ethan R. Elenberg , Rajiv Khanna , Alexandros G. Dimakis , Sahand Negahban

This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…

Optimization and Control · Mathematics 2023-10-04 Xiaoxue Jiang

We consider the maximization problem in the value oracle model of functions defined on $k$-tuples of sets that are submodular in every orthant and $r$-wise monotone, where $k\geq 2$ and $1\leq r\leq k$. We give an analysis of a…

Data Structures and Algorithms · Computer Science 2016-08-05 Justin Ward , Stanislav Zivny

The optimization of submodular functions on the integer lattice has received much attention recently, but the objective functions of many applications are non-submodular. We provide two approximation algorithms for maximizing a…

Data Structures and Algorithms · Computer Science 2018-05-21 Alan Kuhnle , J. David Smith , Victoria G. Crawford , My T. Thai

A number of recent results on optimization problems involving submodular functions have made use of the multilinear relaxation of the problem. These results hold typically in the value oracle model, where the objective function is…

Data Structures and Algorithms · Computer Science 2013-01-31 Jan Vondrak

We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…

Data Structures and Algorithms · Computer Science 2010-06-02 Zoya Svitkina , Lisa Fleischer

With the extensive application of submodularity, its generalizations are constantly being proposed. However, most of them are tailored for special problems. In this paper, we focus on quasi-submodularity, a universal generalization, which…

Data Structures and Algorithms · Computer Science 2014-11-14 Jincheng Mei , Kang Zhao , Bao-Liang Lu

This paper studies the problem of maximizing a monotone submodular function under an unknown knapsack constraint. A solution to this problem is a policy that decides which item to pack next based on the past packing history. The robustness…

Data Structures and Algorithms · Computer Science 2024-10-25 Max Klimm , Martin Knaack

We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a…

Data Structures and Algorithms · Computer Science 2024-11-19 Thibaut Horel , Yaron Singer

Submodular maximization has found extensive applications in various domains within the field of artificial intelligence, including but not limited to machine learning, computer vision, and natural language processing. With the increasing…

Data Structures and Algorithms · Computer Science 2024-12-04 Shuang Cui , Kai Han , Jing Tang , Xueying Li , Aakas Zhiyuli , Hanxiao Li

We consider a robust formulation, introduced by Krause et al. (2008), of the classical cardinality constrained monotone submodular function maximization problem, and give the first constant factor approximation results. The robustness…

Data Structures and Algorithms · Computer Science 2018-10-31 James B. Orlin , Andreas S. Schulz , Rajan Udwani

In this paper, we apply a Threshold-Decreasing Algorithm to maximize $k$-submodular functions under a matroid constraint, which reduces the query complexity of the algorithm compared to the greedy algorithm with little loss in approximation…

Data Structures and Algorithms · Computer Science 2023-07-27 Shuxian Niu , Qian Liu , Yang Zhou , Min Li

The greedy algorithm for monotone submodular function maximization subject to cardinality constraint is guaranteed to approximate the optimal solution to within a $1-1/e$ factor. Although it is well known that this guarantee is essentially…

Data Structures and Algorithms · Computer Science 2022-02-15 Aviad Rubinstein , Junyao Zhao