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Optimization Methods and Software Vol. 00, No. 00, October 2009, 123

Summary: Optimization Methods and Software
Vol. 00, No. 00, October 2009, 1­23
Interior Proximal Algorithm with Variable Metric for
Second-Order Cone Programming: Applications to Structural
Optimization and Support Vector Machines
Felipe Alvarez
, Julio L´opez
and H´ector Ram´irez C.

Departamento de Ingenier´ia Matem´atica, Centro de Modelamiento Matem´atico (CNRS
UMI 2807), FCFM, Universidad de Chile, Blanco Encalada 2120, Santiago, Chile
(Received 30 October 2008)
In this work, we propose an inexact interior proximal type algorithm for solving convex
second-order cone programs. This kind of problems consists of minimizing a convex function
(possibly nonsmooth) over the intersection of an affine linear space with the Cartesian
product of second-order cones. The proposed algorithm uses a variable metric, which is
induced by a class of positive definite matrices, and an appropriate choice of a regularization
parameter. This choice ensures the well-definedness of the proximal algorithm and forces
the iterates to belong to the interior of the feasible set. Also, under suitable assumptions,
it is proven that each limit point of the sequence generated by the algorithm solves the


Source: Alvarez, Felipe - Departamento de Ingeniería Matemática, Universidad de Chile


Collections: Mathematics; Engineering