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

G. Zhou, K.C. Toh and D. Sun
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G. Zhou: Curtin University of Technology
K.C. Toh: National University of Singapore
D. Sun: National University of Singapore

Journal of Optimization Theory and Applications, 2003, vol. 119, issue 2, No 7, 357-377

Abstract: 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.

Keywords: Sum of norms; strict complementarity; quadratic convergence (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/B:JOTA.0000005450.58251.6d

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