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A geometrical insight on pseudoconvexity and pseudomonotonicity

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Abstract

Generalised convexity is revisited from a geometric point of view. A substitute to the subdifferential is proposed. Then generalised monotonicity is considered. A representation of generalised monotone maps allows us to obtain a symmetry between maps and their inverses. Finally, maximality of generalised monotone maps is analysed.

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Authors and Affiliations

  1. LIMOS, Université Blaise Pascal, Clermont, France

    Jean-Pierre Crouzeix

  2. Mathematics, Royal Melbourne Institute of Technology, Melbourne, VIC, Australia

    Andrew Eberhard

  3. Judge Business School, University of Cambridge, Cambridge, UK

    Daniel Ralph

Authors
  1. Jean-Pierre Crouzeix
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  2. Andrew Eberhard
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  3. Daniel Ralph
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Correspondence to Jean-Pierre Crouzeix.

Additional information

This work has been made possible thanks to ARC project DP0664423. The first author thanks RMIT for its hospitality in February 2007.

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Crouzeix, JP., Eberhard, A. & Ralph, D. A geometrical insight on pseudoconvexity and pseudomonotonicity. Math. Program. 123, 61–83 (2010). https://doi.org/10.1007/s10107-009-0324-3

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  • DOI: https://doi.org/10.1007/s10107-009-0324-3

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