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Methods for calculatingl p -minimum norm solutions of consistent linear systems

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Abstract

This paper describes, analyzes, and tests methods for solvingl p -minimum norm problems of the form

$$\min \left\| x \right\|_p^p /p,s.t.Ax = b,$$

where 1<p<∞ andA x=b is a consistent system of linear equations. The paper presents a primal Newton method for problems withp>2 and a dual Newton method that is suitable when 1<p<2. Primaldual methods are also introduced. Numerical experiments illustrate the usefulness of the proposed methods.

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Authors and Affiliations

  1. Hydrological Service, Jerusalem, Israel

    A. Dax (Staff Member)

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  1. A. Dax
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Communicated by D. G. Luenberger

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Dax, A. Methods for calculatingl p -minimum norm solutions of consistent linear systems. J Optim Theory Appl 83, 333–354 (1994). https://doi.org/10.1007/BF02190061

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