Penalty-Type Functions

  • Alexander Rubinov
  • Xiaoqi Yang
Part of the Applied Optimization book series (APOP, volume 85)


Recall that a relation ≥ defined on a set X is called pre-order if (i) xx, for all xX, and (ii) xy and yz imply xz. If x ≥ y and yx, then x and y are called equivalent elements. A pre-order relation is called complete if, for any two elements x and y, either xy or yx.




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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Alexander Rubinov
    • 1
  • Xiaoqi Yang
    • 2
  1. 1.School of Information Technology and Mathematical SciencesUniversity of BallaratVictoriaAustralia
  2. 2.Department of Applied MathematicsHong Kong Polytechnic UniversityHong KongChina

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