Smoothing Newton Method for Minimizing the Sum of p-Norms

S. H. Pan () and Y. X. Jiang
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S. H. Pan: South China University of Technology
Y. X. Jiang: Dalian Jiaotong University

Journal of Optimization Theory and Applications, 2008, vol. 137, issue 2, No 1, 255-275

Abstract: Abstract Consider the problem of minimizing the sum of p-norms, where p is a fixed real number in the interval [1,2]. This nondifferentiable problem arises in many applications, including the VLSI (very-large-scale-integration) layout problem, the facilities location problem and the Steiner minimum tree problem under a given topology. In this paper, we establish the optimality conditions, duality and uniqueness results for the problem. We then present a smoothing Newton method by the semismooth equations which are derived from the optimality conditions. The method is globally and superlinearly convergent, and moreover, it is quadratically convergent when p∈[1,3/2]∪{2}. Particularly, the quadratic convergence is proved for the case wherep∈(1,3/2]∪{2} without requiring strict complementarity. Preliminary numerical results are reported, which indicate that the method proposed is extremely promising.

Keywords: Sum of p-norms; Semismoothness; Smoothing Newton method (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10957-008-9364-8

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