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Multilevel (Hierarchical) Optimization: Complexity Issues, Optimality Conditions, Algorithms

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Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 17))

Summary

In this chapter we discuss some algorithmic and theoretical results on multilevel programming including complexity issues, optimality conditions, and algorithmic methods for solving multilevel programming problems. We also discuss an approach, which is called the multivariate partition approach, for solving a single-level mathematical programming problem based on its equivalent multilevel programming formulation.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, 32611, Gainesville, FL, U.S.A

    Altannar Chinchuluun

  2. Department of Industrial Engineering, Tsinghua University,  , U.S.A

    Hong-Xuan Huang

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  1. Altannar Chinchuluun
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  2. Panos M. Pardalos
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  3. Hong-Xuan Huang
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Correspondence to Altannar Chinchuluun .

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Editors and Affiliations

  1. Dept. Mathematics, Virginia Tech, McBryde Hall 524, Blacksburg, 24061, U.S.A.

    David Y. Gao

  2. State University, Dept. Industrial & Systems Engineering, Virginia Polytechnic Institute &, Whittemore Hall 547, Blacksburg, 24061, U.S.A.

    Hanif D. Sherali

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Chinchuluun, A., Pardalos, P.M., Huang, HX. (2009). Multilevel (Hierarchical) Optimization: Complexity Issues, Optimality Conditions, Algorithms. In: Gao, D., Sherali, H. (eds) Advances in Applied Mathematics and Global Optimization. Advances in Mechanics and Mathematics, vol 17. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-75714-8_6

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