Journal of Global Optimization

, Volume 33, Issue 3, pp 369–391 | Cite as

On the Finite Termination of an Entropy Function Based Non-Interior Continuation Method for Vertical Linear Complementarity Problems

  • Shu-Cherng Fang
  • Jiye Han
  • Zheng-Hai Huang
  • Ş. İlker Bİrbİl


By using a smooth entropy function to approximate the non-smooth max-type function, a vertical linear complementarity problem (VLCP) can be treated as a family of parameterized smooth equations. A Newton-type method with a testing procedure is proposed to solve such a system. We show that under some milder than usual assumptions the proposed algorithm finds an exact solution of VLCP in a finite number of iterations. Some computational results are included to illustrate the potential of this approach.


Entropy function Finite termination Non-interior continuation method Vertical linear complementarity problems Smoothing approximation 

Mathematics Subject Classification

90C33 65K10 


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Copyright information

© Springer 2005

Authors and Affiliations

  • Shu-Cherng Fang
    • 1
    • 2
  • Jiye Han
    • 3
  • Zheng-Hai Huang
    • 4
  • Ş. İlker Bİrbİl
    • 5
  1. 1.Industrial Engineering and Operations ResearchNorth Carolina State UniversityRaleighUSA
  2. 2.Mathematical Sciences and Industrial EngineeringTsinghua UniversityBeijingP.R. China
  3. 3.Institute of Applied Mathematics, Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijingP.R. China
  4. 4.Department of Mathematics, School of ScienceTianjin UniversityTianjinP.R. China
  5. 5.Faculty of Engineering and Natural SciencesSabancı UniversityIstanbulTurkey

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