@inproceedings{8c746dbd12b440b08b8b7355d32881e0,
title = "Online Algorithms for Covering and Packing Problems with Convex Objectives",
abstract = "We present online algorithms for covering and packing problems with (non-linear) convex objectives. The convex covering problem is defined as: minxαRn+f(x) s.t. Ax ≥ 1, where f:Rn+ → R+ is a monotone convex function, and A is an m×n matrix with non-negative entries. In the online version, a new row of the constraint matrix, representing a new covering constraint, is revealed in each step and the algorithm is required to maintain a feasible and monotonically non-decreasing assignment x over time. We also consider a convex packing problem defined as: maxyαRm+ Σ mj=1 yj - g(AT y), where g:Rn+→R+ is a monotone convex function. In the online version, each variable yj arrives online and the algorithm must decide the value of yj on its arrival. This represents the Fenchel dual of the convex covering program, when g is the convex conjugate of f. We use a primal-dual approach to give online algorithms for these generic problems, and use them to simplify, unify, and improve upon previous results for several applications.",
keywords = "Convex optimization, Online algorithm, Primal-dual algorithm",
author = "Yossi Azar and Niv Buchbinder and Chan, \{T. H.Hubert\} and Shahar Chen and Cohen, \{Ilan Reuven\} and Anupam Gupta and Zhiyi Huang and Ning Kang and Viswanath Nagarajan and Joseph Naor and Debmalya Panigrahi",
note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 ; Conference date: 09-10-2016 Through 11-10-2016",
year = "2016",
month = dec,
day = "14",
doi = "10.1109/FOCS.2016.24",
language = "الإنجليزيّة",
series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",
publisher = "IEEE Computer Society",
pages = "148--157",
booktitle = "Proceedings - 57th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016",
address = "الولايات المتّحدة",
}