We obtain a new class of primal affine algorithms for the linearly constrained convex programming. It is constructed from a family of metrics generated the r power, r>=1, of the diagonal iterate vector matrix. We obtain the so called weak convergence. That class contains, as particular cases, the multiplicative Eggermont algorithm for the minimization of a convex function on the positive orthant, when r=1, and the affine scaling Gonzaga and Carlos direction for the general problem, corresponding to r=2. The last author obtained some weaker properties, and the weak convergence for Eggermont method was obtained by Iussem.
T. R. 576-02, PESC/COPPE, Federal University of Rio de Janeiro, 04/2002