Quadratic programming and combinatorial minimum weight product problems

  • Authors:

  • Walter Kern;Gerhard Woeginger

  • Affiliations:

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

  • Venue:
  • Mathematical Programming: Series A and B
  • Year:
  • 2007

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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.