# Online Packing and Covering Framework with Convex Objectives

@article{Buchbinder2014OnlinePA, title={Online Packing and Covering Framework with Convex Objectives}, author={Niv Buchbinder and Shahar Chen and Anupam Gupta and Viswanath Nagarajan and Joseph Naor}, journal={ArXiv}, year={2014}, volume={abs/1412.8347} }

We consider online fractional covering problems with a convex objective, where the covering constraints arrive over time. Formally, we want to solve $\min\,\{f(x) \mid Ax\ge \mathbf{1},\, x\ge 0\},$ where the objective function $f:\mathbb{R}^n\rightarrow \mathbb{R}$ is convex, and the constraint matrix $A_{m\times n}$ is non-negative. The rows of $A$ arrive online over time, and we wish to maintain a feasible solution $x$ at all times while only increasing coordinates of $x$. We also consider…

## 17 Citations

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Improved online algorithms for non-uniform buy-at-bulk network design and the first online algorithm for throughput maximization under $\ell_p$-norm edge capacities are obtained.

### Online Algorithms for Covering and Packing Problems with Convex Objectives

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A primal-dual approach is used to give online algorithms for covering and packing problems with (non-linear) convex objectives, and these algorithms are used to simplify, unify, and improve upon previous results for several applications.

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