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Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…

Machine Learning · Computer Science 2020-06-17 Grigory Malinovsky , Dmitry Kovalev , Elnur Gasanov , Laurent Condat , Peter Richtárik

Fair facility location problems try to balance access costs to open facilities borne by different groups of people by minimizing the $L_p$ norm of these group distances. However, there is no clear choice of "$p$" in the current literature.…

Data Structures and Algorithms · Computer Science 2024-06-21 Swati Gupta , Jai Moondra , Mohit Singh

The paper presents a new approach to solve multifacility location problems, which is based on mixed integer programming and algorithms for minimizing differences of convex (DC) functions. The main challenges for solving the multifacility…

Optimization and Control · Mathematics 2020-02-05 Anuj Bajaj , Boris Mordukhovich , Nguyen Mau Nam , Tuyen Tran

This paper presents novel algorithms for the Fermat-Weber Location Problem, guiding an autonomous agent to the point that minimizes the weighted sum of Euclidean distances to some beacons using only bearing measurements. The existing…

Systems and Control · Electrical Eng. & Systems 2024-10-25 Nhat-Minh Le-Phan , Phuoc Doan Nguyen , Hyo-Sung Ahn , Minh Hoang Trinh

The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization…

Optimization and Control · Mathematics 2011-01-04 Donald Goldfarb , Shiqian Ma

We consider single-machine scheduling problems that are natural generalizations or variations of the min-sum set cover problem and the min-sum vertex cover problem. For each of these problems, we give new approximation algorithms. Some of…

Data Structures and Algorithms · Computer Science 2020-01-22 Felix Happach , Andreas S. Schulz

We consider a facility location problem, where the objective is to ``disperse'' a number of facilities, i.e., select a given number k of locations from a discrete set of n candidates, such that the average distance between selected…

Data Structures and Algorithms · Computer Science 2007-05-23 Sandor P. Fekete , Henk Meijer

We investigate the Fermat-Torricelli problem in d-dimensional real normed spaces or Minkowski spaces, mainly for d=2. Our approach is to study the Fermat-Torricelli locus in a geometric way. We present many new results, as well as give an…

Optimization and Control · Mathematics 2007-07-18 Horst Martini , Konrad J Swanepoel , Gunter Weiss

The classic online facility location problem deals with finding the optimal set of facilities in an online fashion when demand requests arrive one at a time and facilities need to be opened to service these requests. In this work, we study…

Data Structures and Algorithms · Computer Science 2025-05-09 Arghya Chakraborty , Rahul Vaze

The Weber location problem is widely used in several artificial intelligence scenarios. However, the gradient of the objective does not exist at a considerable set of singular points. Recently, a de-singularity subgradient method has been…

Optimization and Control · Mathematics 2025-02-04 Zhao-Rong Lai , Xiaotian Wu , Liangda Fang , Ziliang Chen , Cheng Li

In this paper, we propose the Ordered Median Tree Location Problem (OMT). The OMT is a single-allocation facility location problem where p facilities must be placed on a network connected by a non-directed tree. The objective is to minimize…

Discrete Mathematics · Computer Science 2025-02-11 Miguel A. Pozo , Justo Puerto , Alberto Torrejon

The recent large scale availability of mobility data, which captures individual mobility patterns, poses novel operational problems that are exciting and challenging. Motivated by this, we introduce and study a variant of the…

Data Structures and Algorithms · Computer Science 2023-12-12 Ozan Candogan , Yiding Feng

The purpose of this paper is to propose and analyze a multi-step iterative algorithm to solve a convex optimization problem and a fixed point problem posed on a Hadamard space. The convergence properties of the proposed algorithm are…

Functional Analysis · Mathematics 2018-02-28 Muhammad Aqeel Ahmad Khan , Hafiza Arham Maqbool

In the classical facility location problem we consider a graph $G$ with fixed weights on the edges of $G$. The goal is then to find an optimal positioning for a set of facilities on the graph with respect to some objective function. We…

Data Structures and Algorithms · Computer Science 2014-06-10 Boaz Ben-Moshe , Michael Elkin , Lee-Ad Gottlieb , Eran Omri

The soft capacitated facility location problem (SCFLP) is a classic combinatorial optimization problem, with its variants widely applied in the fields of operations research and computer science. In the SCFLP, given a set $\mathcal{F}$ of…

Data Structures and Algorithms · Computer Science 2025-02-18 Hanyin Xiao , Jiaming Zhang , Zhikang Zhang , Weidong Li

In this paper we analyze the extension of the classical smallest enclosing disk problem to the case of the location of a polyellipsoid to fully cover a set of demand points in $\mathbb{R}^d$. We prove that the problem is polynomially…

Optimization and Control · Mathematics 2021-01-12 Víctor Blanco , Justo Puerto

In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. This problem minimizes a monotone ordered weighted median function of the distances between given demand points in $\mathbb{R}^d$ and its closest…

Optimization and Control · Mathematics 2021-08-03 Víctor Blanco , Ricardo Gázquez , Diego Ponce , Justo Puerto

We investigate a location-allocation-routing problem where trucks deliver goods from a central production facility to a set of warehouses with fixed locations and known demands. Due to limited capacities congestion occurs and results in…

Optimization and Control · Mathematics 2022-08-09 Vanessa Lange , Hans Daduna

$ $In many optimization problems, a feasible solution induces a multi-dimensional cost vector. For example, in load-balancing a schedule induces a load vector across the machines. In $k$-clustering, opening $k$ facilities induces an…

Data Structures and Algorithms · Computer Science 2018-11-14 Deeparnab Chakrabarty , Chaitanya Swamy

The subspace approximation problem Subspace($k$,$p$) asks for a $k$-dimensional linear subspace that fits a given set of points optimally, where the error for fitting is a generalization of the least squares fit and uses the $\ell_{p}$ norm…

Data Structures and Algorithms · Computer Science 2011-01-04 Amit Deshpande , Kasturi Varadarajan , Madhur Tulsiani , Nisheeth K. Vishnoi