Quantified linear programs: a computational study

  • Authors:

  • Thorsten Ederer;Ulf Lorenz;Alexander Martin;Jan Wolf

  • Affiliations:

  • Institute of Mathematics, Technische Universität Darmstadt, Germany;Institute of Mathematics, Technische Universität Darmstadt, Germany;Institute of Mathematics, Universität Erlangen-Nürnberg, Germany;Institute of Mathematics, Technische Universität Darmstadt, Germany

  • Venue:
  • ESA'11 Proceedings of the 19th European conference on Algorithms
  • Year:
  • 2011

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Abstract

Quantified linear programs (QLPs) are linear programs with variables being either existentially or universally quantified. The integer variant (QIP) is PSPACE-complete, and the problem is similar to games like chess, where an existential and a universal player have to play a two-person-zero-sum game. At the same time, a QLP with n variables is a variant of a linear program living in Rn, and it has strong similarities with multi-stage stochastic linear programs with variable right-hand side. Our interest in QLPs stems from the fact that they are LP-relaxations of QIPs, which themselves are mighty modeling tools. In order to solve QLPs, we apply a nested decomposition algorithm. In a detailed computational study, we examine, how different structural properties like the number of universal variables, the number of universal variable blocks as well as their positions in the QLP influence the solution process.