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Reducing Exhausters

Author

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  • V. Roshchina

    (City University of Hong Kong)

Abstract

The notions of upper and lower exhausters were introduced by Demyanov (Optimization 45:13–29, 1999). Upper and lower exhausters can be employed to study a very wide range of positively homogeneous functions, for example, various directional derivatives of nonsmooth functions. Exhausters are not uniquely defined; hence, the problem of minimality arises naturally. This paper describes some techniques for reducing exhausters, both in size and amount of sets. We define also a modified convertor which provides much more flexibility in converting upper exhausters to lower ones and vice versa, and allows us to obtain much smaller sets.

Suggested Citation

  • V. Roshchina, 2008. "Reducing Exhausters," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 261-273, February.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:2:d:10.1007_s10957-007-9296-8
    DOI: 10.1007/s10957-007-9296-8
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