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• W1574339078 abstract "We consider online fractional covering problems with a convex objective, where the covering constraints arrive over time. Formally, we want to solve $min,{f(x) mid Axge mathbf{1},, xge 0},$ where the objective function $f:mathbb{R}^nrightarrow mathbb{R}$ is convex, and the constraint matrix $A_{mtimes n}$ 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 dual packing problems of the form $max,{c^intercal y - g(mu) mid A^intercal y le mu,, yge 0}$, where $g$ is a convex function. In the online setting, variables $y$ and columns of $A^intercal$ arrive over time, and we wish to maintain a non-decreasing solution $(y,mu)$. We provide an online primal-dual framework for both classes of problems with competitive ratio depending on certain monotonicity and smoothness parameters of $f$; our results match or improve on guarantees for some special classes of functions $f$ considered previously. Using this fractional solver with problem-dependent randomized rounding procedures, we obtain competitive algorithms for the following problems: online covering LPs minimizing $ell_p$-norms of arbitrary packing constraints, set cover with multiple cost functions, capacity constrained facility location, capacitated multicast problem, set cover with set requests, and profit maximization with non-separable production costs. Some of these results are new and others provide a unified view of previous results, with matching or slightly worse competitive ratios." @default.
• W1574339078 created "2016-06-24" @default.
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• W1574339078 date "2014-12-29" @default.
• W1574339078 modified "2023-09-27" @default.
• W1574339078 title "Online Packing and Covering Framework with Convex Objectives" @default.
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• W1574339078 hasPublicationYear "2014" @default.
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