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Complementarity problems with respect to Loewnerian cones

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  • Alberto Seeger
  • David Sossa

Abstract

This work deals with the analysis and numerical resolution of a broad class of complementarity problems on spaces of symmetric matrices. The complementarity conditions are expressed in terms of the Loewner ordering or, more generally, with respect to a dual pair of Loewnerian cones. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Alberto Seeger & David Sossa, 2015. "Complementarity problems with respect to Loewnerian cones," Journal of Global Optimization, Springer, vol. 62(2), pages 299-318, June.
    • Handle: RePEc:spr:jglopt:v:62:y:2015:i:2:p:299-318
    DOI: 10.1007/s10898-014-0230-y
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    References listed on IDEAS

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    1. Defeng Sun & Jie Sun, 2002. "Semismooth Matrix-Valued Functions," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 150-169, February.
    2. Pedro Gajardo & Alberto Seeger, 2012. "Reconstructing a matrix from a partial sampling of Pareto eigenvalues," Computational Optimization and Applications, Springer, vol. 51(3), pages 1119-1135, April.
    3. Ryoichi Nishimura & Shunsuke Hayashi & Masao Fukushima, 2012. "Semidefinite complementarity reformulation for robust Nash equilibrium problems with Euclidean uncertainty sets," Journal of Global Optimization, Springer, vol. 53(1), pages 107-120, May.
    4. 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.
    5. Jean-Baptiste Hiriart-Urruty & Jérôme Malick, 2012. "A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 551-577, June.
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