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A Decomposition-Based Global Optimization Approach for Solving Bilevel Linear and Quadratic Programs

  • V. Visweswaran
  • C. A. Floudas
  • M. G. Ierapetritou
  • E. N. Pistikopoulos
Chapter
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 7)

Abstract

The paper presents a decomposition based global optimization approach to bilevel linear and quadratic programming problems. By replacing the inner problem by its corresponding KKT optimality conditions, the problem is transformed to a single yet non-convex, due to the complementarity condition, mathematical program. Based on the primal-dual global optimization approach of Floudas and Visweswaran (1990, 1993), the problem is decomposed into a series of primal and relaxed-dual subproblems whose solutions provide lower and upper bounds to the global optimum. By further exploiting the special structure of the bilevel problem, new properties are established which enable the efficient implementation of the proposed algorithm. Computational results are reported for both linear and quadratic example problems.

Keywords

Dual Problem Lagrange Function Primal Problem Bilevel Program Bilevel Program Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • V. Visweswaran
    • 1
    • 2
  • C. A. Floudas
    • 1
  • M. G. Ierapetritou
    • 3
  • E. N. Pistikopoulos
    • 3
  1. 1.Department of Chemical EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Mobil Research and Development CorporationPenningtonUSA
  3. 3.Centre for Process Systems Engineering, Department of Chemical EngineeringImperial CollegeLondonUK

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