Computational Optimization and Applications

, Volume 45, Issue 3, pp 557–579

Smoothing algorithms for complementarity problems over symmetric cones

Article

Abstract

There recently has been much interest in studying optimization problems over symmetric cones. In this paper, we first investigate a smoothing function in the context of symmetric cones and show that it is coercive under suitable assumptions. We then extend two generic frameworks of smoothing algorithms to solve the complementarity problems over symmetric cones, and prove the proposed algorithms are globally convergent under suitable assumptions. We also give a specific smoothing Newton algorithm which is globally and locally quadratically convergent under suitable assumptions. The theory of Euclidean Jordan algebras is a basic tool which is extensively used in our analysis. Preliminary numerical results for second-order cone complementarity problems are reported.

Keywords

Complementarity problem Symmetric cone Euclidean Jordan algebra Smoothing algorithm Merit function method 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Mathematics, School of ScienceTianjin UniversityTianjinPeople’s Republic of China

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