Abstract
We study general mixed fractional packing and covering problems (MPC ε ) 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).
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Jansen, K. (2005). Approximation Algorithms for Mixed Fractional Packing and Covering Problems. In: Persiano, G., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2004. Lecture Notes in Computer Science, vol 3351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31833-0_2
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DOI: https://doi.org/10.1007/978-3-540-31833-0_2
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