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

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Book cover State of the Art in Global Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((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.

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Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544, USA

    V. Visweswaran & C. A. Floudas

  2. Mobil Research and Development Corporation, Pennington, NJ, 08534, USA

    V. Visweswaran

  3. Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College, London, SW7 2BY, UK

    M. G. Ierapetritou & E. N. Pistikopoulos

Authors
  1. V. Visweswaran
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  2. C. A. Floudas
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  3. M. G. Ierapetritou
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  4. E. N. Pistikopoulos
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Editor information

Editors and Affiliations

  1. Princeton University, USA

    C. A. Floudas

  2. University of Florida, USA

    P. M. Pardalos

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© 1996 Kluwer Academic Publishers

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Visweswaran, V., Floudas, C.A., Ierapetritou, M.G., Pistikopoulos, E.N. (1996). A Decomposition-Based Global Optimization Approach for Solving Bilevel Linear and Quadratic Programs. In: Floudas, C.A., Pardalos, P.M. (eds) State of the Art in Global Optimization. Nonconvex Optimization and Its Applications, vol 7. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3437-8_10

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  • DOI: https://doi.org/10.1007/978-1-4613-3437-8_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3439-2

  • Online ISBN: 978-1-4613-3437-8

  • eBook Packages: Springer Book Archive

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