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MINLP Optimization Using Simplicial Approximation Method for Classes of Non-Convex Problems

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Frontiers in Global Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 74))

Abstract

Significant advances have been made in the last two decades for the effective solution of Mixed Integer Non-Linear Programming (MINLP) problems, mainly by exploiting the special structure of the problem that results under certain convexity assumptions. A number of decomposition based algorithms have been developed based on the concepts of projection, outer approximation and relaxation. For the case of non-convex MINLPs a number of deterministic global optimization algorithms have been introduced mainly based on branch and bound strategies. In this paper we present a novel decomposition algorithm to solve MINLP problems under the assumptions that the objective function is convex, the set of equality and inequality constraints are either convex, concave or quasi-concave functions and are continuous and once differentiable. The proposed approach is based on the idea of closely approximating the feasible region defined by the set of constraints by a convex polytope using the simplicial approximation approach. Convergence of the algorithm along with a number of computational examples are presented illustrating the applicability and efficiency of the proposed approach.

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Authors and Affiliations

  1. Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, NJ, 08854, USA

    Vishal Goyal & Marianthi G. Ierapetritou

Authors
  1. Vishal Goyal
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  2. Marianthi G. Ierapetritou
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Correspondence to Marianthi G. Ierapetritou .

Editor information

Editors and Affiliations

  1. Princeton University, USA

    C. A. Floudas

  2. University of Florida, USA

    Panos Pardalos

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© 2004 Kluwer Academic Publishers

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Goyal, V., Ierapetritou, M.G. (2004). MINLP Optimization Using Simplicial Approximation Method for Classes of Non-Convex Problems. In: Floudas, C.A., Pardalos, P. (eds) Frontiers in Global Optimization. Nonconvex Optimization and Its Applications, vol 74. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0251-3_10

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  • DOI: https://doi.org/10.1007/978-1-4613-0251-3_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7961-4

  • Online ISBN: 978-1-4613-0251-3

  • eBook Packages: Springer Book Archive

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