  We generalize the fractional packing framework of Garg and Koenemann to the
case of linear fractional packing problems over polyhedral cones. More
precisely, we provide approximation algorithms for problems of the form
$\max\{c^T x : Ax \leq b, x \in C \}$, where the matrix $A$ contains no
negative entries and $C$ is a cone that is generated by a finite set $S$ of
non-negative vectors. While the cone is allowed to require an exponential-sized
representation, we assume that we can access it via one of three types of
oracles. For each of these oracles, we present positive results for the
approximability of the packing problem. In contrast to other frameworks, the
presented one allows the use of arbitrary linear objective functions and can be
applied to a large class of packing problems without much effort. In
particular, our framework instantly allows to derive fast and simple fully
polynomial-time approximation algorithms (FPTASs) for a large set of network
flow problems, such as budget-constrained versions of traditional network
flows, multicommodity flows, or generalized flows. Some of these FPTASs
represent the first ones of their kind, while others match existing results but
offer a much simpler proof.
