Geodesic
Regularization and normal solutions of systems of linear equations and inequalities
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 113-121 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper provides some examples of mutually dual unconstrained optimization problems originating from regularization problems for systems of linear equations and/or inequalities. The solution of each of these mutually dual problems can be found from the solution of the other problem by means of simple formulas. Since mutually dual problems have different dimensions, it is natural to solve the unconstrained optimization problems with smaller dimension.
Keywords: regularization, piecewise quadratic function, unconstrained optimization, mutually dual problems, generalized Newton method. 
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A. I. Golikov; Yu. G. Evtushenko. Regularization and normal solutions of systems of linear equations and inequalities. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 2, pp. 113-121. http://geodesic.mathdoc.fr/item/TIMM_2014_20_2_a9/

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