Mathematical Programming

, Volume 36, Issue 3, pp 307–339 | Cite as

An outer-approximation algorithm for a class of mixed-integer nonlinear programs

  • Marco A. Duran
  • Ignacio E. Grossmann


An outer-approximation algorithm is presented for solving mixed-integer nonlinear programming problems of a particular class. Linearity of the integer (or discrete) variables, and convexity of the nonlinear functions involving continuous variables are the main features in the underlying mathematical structure. Based on principles of decomposition, outer-approximation and relaxation, the proposed algorithm effectively exploits the structure of the problems, and consists of solving an alternating finite sequence of nonlinear programming subproblems and relaxed versions of a mixed-integer linear master program. Convergence and optimality properties of the algorithm are presented, as well as a general discussion on its implementation. Numerical results are reported for several example problems to illustrate the potential of the proposed algorithm for programs in the class addressed in this paper. Finally, a theoretical comparison with generalized Benders decomposition is presented on the lower bounds predicted by the relaxed master programs.

Key words

Mixed-integer nonlinear programming outer-approximation decomposition cutting planes computer-aided design 


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Copyright information

© The Mathematical Programming Society, Inc. 1986

Authors and Affiliations

  • Marco A. Duran
    • 1
  • Ignacio E. Grossmann
    • 1
  1. 1.Department of Chemical EngineeringCarnegie-Mellon UniversityPittsburghUSA

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