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A new class of potential affine algorithms for linear convex programming

A. W. Martins Pinto (apihngora***at***bol.com.br)
P. Roberto Oliveira (poliveir***at***cos.ufrj.br)
J.. Xavier da Cruz Neto (jxavier***at***ufpi.br)

Abstract: 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.

Keywords: Interior Point Methods, Projection algorithms

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: T. R. 576-02, PESC/COPPE, Federal University of Rio de Janeiro, 04/2002


Entry Submitted: 04/26/2002
Entry Accepted: 04/26/2002
Entry Last Modified: 04/28/2005

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