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Globally and Quadratically Convergent Algorithm for Minimizing the Sum of Euclidean Norms

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  • G. Zhou

    (Curtin University of Technology)

  • K.C. Toh

    (National University of Singapore)

  • D. Sun

    (National University of Singapore)

Abstract

For the problem of minimizing the sum of Euclidean norms (MSN), most existing quadratically convergent algorithms require a strict complementarity assumption. However, this assumption is not satisfied for a number of MSN problems. In this paper, we present a globally and quadratically convergent algorithm for the MSN problem. In particular, the quadratic convergence result is obtained without assuming strict complementarity. Examples without strictly complementary solutions are given to show that our algorithm can indeed achieve quadratic convergence. Preliminary numerical results are reported.

Suggested Citation

  • G. Zhou & K.C. Toh & D. Sun, 2003. "Globally and Quadratically Convergent Algorithm for Minimizing the Sum of Euclidean Norms," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 357-377, November.
    • Handle: RePEc:spr:joptap:v:119:y:2003:i:2:d:10.1023_b:jota.0000005450.58251.6d
    DOI: 10.1023/B:JOTA.0000005450.58251.6d
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    References listed on IDEAS

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    1. Stephen M. Robinson, 1992. "Normal Maps Induced by Linear Transformations," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 691-714, August.
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