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We use the proximal point method with the ϕ-divergence given by ϕ(t) = t−log t− 1 for the minimization of quasiconvex functions subject to nonnegativity constraints. We establish that the sequence generated by our algorithm is well-defined in the sense that it exists and it is not cyclical. Without any assumption of boundedness level to the objective… (More)

- F. G. M. CUNHA, A. W. M. PINTO, P. R. OLIVEIRA, X. da C. NETO
- 2005

We obtain a new class of primal affine scaling algorithms for the linearly constrained convex programming. It is constructed through a family of metrics generated by −r power, r ≥ 1, of the diagonal iterate vector matrix. We prove the so-called weak convergence. It generalizes some known algorithms. Working in dual space, we generalize the dual affine… (More)

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