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Lipschitz Continuity of the Solution Mapping of Symmetric Cone Complementarity Problems

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  • Xin-He Miao
  • Jein-Shan Chen

Abstract

This paper investigates the Lipschitz continuity of the solution mapping of symmetric cone (linear or nonlinear) complementarity problems (SCLCP or SCCP, resp.) over Euclidean Jordan algebras. We show that if the transformation has uniform Cartesian P‐property, then the solution mapping of the SCCP is Lipschitz continuous. Moreover, we establish that the monotonicity of mapping and the Lipschitz continuity of solutions of the SCLCP imply ultra P‐property, which is a concept recently developed for linear transformations on Euclidean Jordan algebra. For a Lyapunov transformation, we prove that the strong monotonicity property, the ultra P‐property, the Cartesian P‐property, and the Lipschitz continuity of the solutions are all equivalent to each other.

Suggested Citation

  • Xin-He Miao & Jein-Shan Chen, 2012. "Lipschitz Continuity of the Solution Mapping of Symmetric Cone Complementarity Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:130682
    DOI: 10.1155/2012/130682
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    References listed on IDEAS

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    3. Lingchen Kong & Levent Tunçel & Naihua Xiu, 2009. "Vector-Valued Implicit Lagrangian For Symmetric Cone Complementarity Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(02), pages 199-233.
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    6. Jiyuan Tao & M. Seetharama Gowda, 2005. "Some P -Properties for Nonlinear Transformations on Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 985-1004, November.
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