Quantified Linear Programs: A Computational Study

  • Thorsten Ederer
  • Ulf Lorenz
  • Alexander Martin
  • Jan Wolf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)


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 \(\hbox{\rm I\kern - 0.15em R}^n\), 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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Thorsten Ederer
    • 1
  • Ulf Lorenz
    • 1
  • Alexander Martin
    • 2
  • Jan Wolf
    • 1
  1. 1.Institute of MathematicsTechnische Universität DarmstadtGermany
  2. 2.Institute of MathematicsUniversität Erlangen-NürnbergGermany

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