Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/6097
 Title: Solving $L_{p}$-Norm Problems and Applications Authors: Li, Yuying Keywords: computer sciencetechnical report Issue Date: Mar-1993 Publisher: Cornell University Citation: http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR93-1331 Abstract: The $l_{p}$ norm discrete estimation problem min$_{x\in\Re^{n}} \Vert b-A^{T} x\Vert^{p}_{p}$ has been solved in many data analysis applications, e.g. geophysical modeling. Recently, a new globally convergent Newton method (called GNCS) has been proposed for solving $l{p}$ problems with 1 $\leq p \leq$ 2 [5]. This method is much faster than the widely used IRLS method when 1 $\leq p \leq$ 1.5 and comparable to it when $p greater than$ 1.5. In this paper, modification is made to the line search prodedure so that the GNCS method is applicable for $l_{p}$ problems with 1 $\leq p less than \infty$. The global convergence results for $l_{1}$ problems are obtained under weaker assumptions than required in [2]. In addition, the usefulness of $l_{p}$ norm solution with 1 $\leq p \leq$ 2 is demonstrated by applying the GNCS algorithm to a synthetic geophysical tomographic inversion problem. Additional numerical results are included to support the efficiency of GNCS. Key Words: linear regression, discrete estimation, tomographic inversion, IRLS, GNCS, linear programming, Newton method. Subject Classification: AMS/MOS: 65H10, 65K05, 65K10. URI: http://hdl.handle.net/1813/6097 Appears in Collections: Computer Science Technical Reports

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