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Conditions for Error Bounds and Bounded Level Sets of Some Merit Functions for the Second-Order Cone Complementarity Problem

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  • J.-S. Chen

    (National Taiwan Normal University
    National Center for Theoretical Sciences)

Abstract

Recently this author studied several merit functions systematically for the second-order cone complementarity problem. These merit functions were shown to enjoy some favorable properties, to provide error bounds under the condition of strong monotonicity, and to have bounded level sets under the conditions of monotonicity as well as strict feasibility. In this paper, we weaken the condition of strong monotonicity to the so-called uniform P *-property, which is a new concept recently developed for linear and nonlinear transformations on Euclidean Jordan algebra. Moreover, we replace the monotonicity and strict feasibility by the so-called R 01 or R 02-functions to keep the property of bounded level sets.

Suggested Citation

  • J.-S. Chen, 2007. "Conditions for Error Bounds and Bounded Level Sets of Some Merit Functions for the Second-Order Cone Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 459-473, December.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9279-9
    DOI: 10.1007/s10957-007-9279-9
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    References listed on IDEAS

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    1. Jein-Shan Chen, 2006. "Two classes of merit functions for the second-order cone complementarity problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 495-519, December.
    2. M. Seetharama Gowda & Roman Sznajder, 2006. "Automorphism Invariance of P - and GUS -Properties of Linear Transformations on Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 109-123, February.
    3. Yong-Jin Liu & Li-Wei Zhang & Yin-He Wang, 2006. "Some Properties Of A Class Of Merit Functions For Symmetric Cone Complementarity Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 473-495.
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    Cited by:

    1. Xin-He Miao & Yu-Lin Chang & Jein-Shan Chen, 2017. "On merit functions for p-order cone complementarity problem," Computational Optimization and Applications, Springer, vol. 67(1), pages 155-173, May.
    2. Xin-He Miao & Shengjuan Guo & Nuo Qi & Jein-Shan Chen, 2016. "Constructions of complementarity functions and merit functions for circular cone complementarity problem," Computational Optimization and Applications, Springer, vol. 63(2), pages 495-522, March.

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