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.


Penalty Function Lower Semicontinuous Exact Penalty Perturbation Function Weak Duality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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