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Quadratic programming and combinatorial minimum weight product problems

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Abstract

We present a fully polynomial time approximation scheme (FPTAS) for minimizing an objective (a T x + γ)(b T x + δ) under linear constraints A x ≤ d. Examples of such problems are combinatorial minimum weight product problems such as the following: given a graph G = (V,E) and two edge weights \({a},{b}: E \rightarrow \mathbb{R}_+\) find an s − t path P that minimizes a(P)b(P), the product of its edge weights relative to a and b.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Mathematics and Computer Science, Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Walter Kern & Gerhard Woeginger

Authors
  1. Walter Kern
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  2. Gerhard Woeginger
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Correspondence to Walter Kern.

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Kern, W., Woeginger, G. Quadratic programming and combinatorial minimum weight product problems. Math. Program. 110, 641–649 (2007). https://doi.org/10.1007/s10107-006-0047-7

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  • DOI: https://doi.org/10.1007/s10107-006-0047-7

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Mathematics Subject Classification (2000)