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2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS) (2016)
New Brunswick, New Jersey, USA
Oct. 9, 2016 to Oct. 11, 2016
ISSN: 0272-5428
ISBN: 978-1-5090-3933-3
pp: 148-157
ABSTRACT
We present online algorithms for covering and packing problems with (non-linear) convex objectives. The convex covering problem is defined as: minxΕRn+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: maxyΕRm+ 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.
INDEX TERMS
Convex functions, Production, Cost function, Computer science, Electronic mail, Linear programming, Routing
CITATION

Y. Azar et al., "Online Algorithms for Covering and Packing Problems with Convex Objectives," 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS), New Brunswick, New Jersey, USA, 2016, pp. 148-157.
doi:10.1109/FOCS.2016.24
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