Conjugate gradient re-weighted optimization

The algorithm of the regularized conjugate gradient method can be summarized as follows  

This method is c allecl the conjugate gradient method with the adaptive regularizat ion. 

1 I hc Tikhovoi ptnmntiric finir.tionnl with a pseudo-quadratic sta.bd.izcr In (diapler 2 W( have demonstiated that, in general cases, a stabilizing functional can be rc prcscniU d in the form of the pseudo-quadratic functional (2.72)  

Finally, for the minimum gradient support functional smgs (ttt), we find 

Therefore, the problem of minimizing the parametric functional, given by equation (5.117), can be treated in a similar way to the minimization of the conventional Tikhonov functional. The only difference is that now we introduce some variable weighting matrix Wg for the model parameters. The minimization problem for the parametric functional introduced by equation (5.117) can be solved using the ideas of traditional gradient-type methods. 

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We call this algorithm conjugate gradient re-weighted optimization because the weighting matrix is updated on every iteration (Portniaguine and Zhdanov,... 

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