Modification of the parametrized method of centers (Q1263525)

A common technique for solving convex programming problems is by reduction to unconstrained minimization of some auxiliary functional. This technique is the basis of the method of centers, the method of penalty functions, and the method of modified Lagrange functions [see \textit{K. Grossmann} and \textit{A. A. Kaplan}, ``Nonlinear programming on the basis of unconditional minimization'' (Russian) (1981; Zbl 0536.90075)]. \textit{Ya. I. Zabotin} [Izv. Vyssh. Uchebn. Zaved., Mat. 19, No.6, 36-43 (1975); English translation in Sov. Math., Dokl. 19, No.6, 28-33 (1975; Zbl 0354.90080)] constructed the auxiliary functional using the maximum function and a technique is proposed for parametrization of this variant of the method of centers. In this paper, we propose an algorithm which is a modification of the parametrized method of centers.