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The Montagne Russe algorithm for global optimization

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  • Jean-Pierre Aubin
  • Laurent Najman

Abstract

The “Montagnes Russes” algorithm for finding the global minima of a lower semi-continuous function (thus involving state constraints) is a descent algorithm applied to an auxiliary function whose local and global minima are the global minima of the original function. Although this auxiliary function decreases along the trajectory of any of its minimizing sequences, the original function jumps above local maxima, leaves local minima, play “Montagnes Russes” (called “American Mountains” in Russian and “Big Dipper” in American!), but, ultimately, converges to its infimum. This auxiliary function is approximated by an increasing sequence of functions defined recursively at each point of the minimizing sequence. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • Jean-Pierre Aubin & Laurent Najman, 1998. "The Montagne Russe algorithm for global optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 153-168, November.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:2:p:153-168
    DOI: 10.1007/s001860050018
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