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Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

Optimization and Control · Mathematics 2023-02-17 Jelena Diakonikolas , Cristóbal Guzmán

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled,…

Optimization and Control · Mathematics 2017-09-18 Andrea Simonetto , Hadi Jamali-Rad

We present a comprehensive framework that unifies several research areas within the context of vertex-weighted bipartite graphs, providing deeper insights and improved solutions. The fundamental solution concept for each problem involves…

Discrete Mathematics · Computer Science 2024-11-06 T-H. Hubert Chan , Quan Xue

In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function,…

Optimization and Control · Mathematics 2019-11-19 Brendan O'Donoghue , Chris J. Maddison

Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…

Optimization and Control · Mathematics 2024-03-12 Tyler Hanks , Matthew Klawonn , Evan Patterson , Matthew Hale , James Fairbanks

Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…

Machine Learning · Computer Science 2013-11-19 Stefanie Jegelka , Francis Bach , Suvrit Sra

We study distributed composite optimization over networks: agents minimize a sum of smooth (strongly) convex functions, the agents' sum-utility, plus a nonsmooth (extended-valued) convex one. We propose a general unified algorithmic…

Optimization and Control · Mathematics 2021-08-04 Jinming Xu , Ye Tian , Ying Sun , Gesualdo Scutari

We propose a new framework that unifies different fairness measures into a general, parameterized class of convex fairness measures suitable for optimization contexts. First, we propose a new class of order-based fairness measures, discuss…

Optimization and Control · Mathematics 2025-01-30 Man Yiu Tsang , Karmel S. Shehadeh

This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…

Optimization and Control · Mathematics 2025-03-14 Zixuan Liu , Xuyang Wu , Dandan Wang , Jie Lu

In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…

Optimization and Control · Mathematics 2019-10-01 Anastasiya Ivanova , Pavel Dvurechensky , Alexander Gasnikov , Dmitry Kamzolov

We study the optimal contract problem in the \emph{combinatorial actions} framework of D\"utting et al.~[FOCS'21], where a principal delegates a project to an agent who chooses a subset of hidden, costly actions, and the resulting reward is…

Computer Science and Game Theory · Computer Science 2026-03-17 Michal Feldman , Liat Yashin

In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it…

Machine Learning · Computer Science 2015-05-08 Bharath Sankaran , Marjan Ghazvininejad , Xinran He , David Kale , Liron Cohen

We develop a framework for the distributed minimization of submodular functions. Submodular functions are a discrete analog of convex functions and are extensively used in large-scale combinatorial optimization problems. While there has…

Optimization and Control · Mathematics 2018-01-23 Hassan Jaleel , Jeff Shamma

Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation…

Machine Learning · Computer Science 2019-05-07 Andrew An Bian , Baharan Mirzasoleiman , Joachim M. Buhmann , Andreas Krause

Submodular functions, as well as the sub-class of decomposable submodular functions, and their optimization appear in a wide range of applications in machine learning, recommendation systems, and welfare maximization. However, optimization…

Data Structures and Algorithms · Computer Science 2024-06-04 Akbar Rafiey

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

We study the problem of minimizing the sum of potentially non-differentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the…

Optimization and Control · Mathematics 2021-02-17 Yankai Lin , Iman Shames , Dragan Nesic

In this paper, we study possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general nonlinear and nonsmooth cone constrained optimization…

Optimization and Control · Mathematics 2024-04-23 M. V. Dolgopolik

We consider fairness in submodular maximization subject to a knapsack constraint, a fundamental problem with various applications in economics, machine learning, and data mining. In the model, we are given a set of ground elements, each…

Data Structures and Algorithms · Computer Science 2025-05-20 Lijun Li , Chenyang Xu , Liuyi Yang , Ruilong Zhang

We show that a broad range of convex optimization algorithms, including alternating projection, operator splitting, and multiplier methods, can be systematically derived from the framework of subspace correction methods via convex duality.…

Optimization and Control · Mathematics 2025-05-16 Boou Jiang , Jongho Park , Jinchao Xu
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