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Modeling, Simulation and Optimization of Complex Processes pp 485–508Cite as

Partly Convex and Convex-Monotonic Optimization Problems

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Summary

A class of nonconvex optimization problems is studied that exhibits partial convexity combined with partial monotonicity. To exploit this particular hybrid structure a natural approach is to use a branch and bound scheme with branching performed on the nonconvex variables and bounds computed by lagrangian or convex relaxation. We discuss conditions that guarantee convergence of such branch and bound algorithms. Incidentally, several incorrect results in the recent literature on related subjects are reviewed.

Key words

  • Nonconvex optimization
  • hybrid convex-monotonic optimization
  • partly convex programming
  • branch and bound method
  • lagrangian relaxation
  • dual bound
  • consistent bound

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  • DOI: 10.1007/3-540-27170-8_37
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Author information

Authors and Affiliations

  1. Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307, Hanoi, Vietnam

    Hoang Tuy

Authors
  1. Hoang Tuy
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Editor information

Editors and Affiliations

  1. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR), Universität Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Hans Georg Bock & Ekaterina Kostina & 

  2. Institute of Mathematics, Vietnamese Academy of Science and Technology (VAST), 18 Hoang Quoc Viet Road, 10307, Hanoi, Vietnam

    Hoang Xuan Phu

  3. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, 68120, Heidelberg, Germany

    Rolf Rannacher

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Tuy, H. (2005). Partly Convex and Convex-Monotonic Optimization Problems. In: Bock, H.G., Phu, H.X., Kostina, E., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27170-8_37

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