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A Smoothing Method with Appropriate Parameter Control Based on Fischer‐Burmeister Function for Second‐Order Cone Complementarity Problems

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  • Yasushi Narushima
  • Hideho Ogasawara
  • Shunsuke Hayashi

Abstract

We deal with complementarity problems over second‐order cones. The complementarity problem is an important class of problems in the real world and involves many optimization problems. The complementarity problem can be reformulated as a nonsmooth system of equations. Based on the smoothed Fischer‐Burmeister function, we construct a smoothing Newton method for solving such a nonsmooth system. The proposed method controls a smoothing parameter appropriately. We show the global and quadratic convergence of the method. Finally, some numerical results are given.

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:830698
DOI: 10.1155/2013/830698
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