Fast approximation algorithms for fractional packing and covering problems
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We study general mixed fractional packing and covering problems (MPCε ) of the following form: Given a vector $f: B \rightarrow {\rm IR}^{M}_{+}$ of M nonnegative continuous convex functions and a vector $g: B \rightarrow {\rm IR}^{M}_{+}$ of M nonnegative continuous concave functions, two M – dimensional nonnegative vectors a,b, a nonempty convex compact set B and a relative tolerance ε ∈ (0,1), find an approximately feasible vector x ∈ B such that f(x) ≤ (1 + ε) a and g(x) ≥ (1 – ε) b or find a proof that no vector is feasible (that satisfies x ∈ B, f(x) ≤ a and g(x) ≥ b).