Journal of Convex Analysis 12 (2005), No. 1, 095--111
Copyright Heldermann Verlag 2005
A Bundle Interior Proximal Method for Solving Convex Minimization Problems
Nguyen Thi Thu Van
Dept. of Mathematics and Computer Sciences, Faculty of Natural Sciences, National University, HoChiMinh City, Vietnam
Van Hien Nguyen
Dép. de Mathématiques, Facultés Universitaires Notre Dame de la Paix, 5000 Namur, Belgium
Jean-Jacques Strodiot
Dép. de Mathématiques, Facultés Universitaires Notre Dame de la Paix, 5000 Namur, Belgium
We extend the standard bundle proximal method for finding the minimum of a convex not necessarily differentiable function on the nonnegative orthant. The strategy consists in approximating the objective function by a piecewise linear convex function and using distance-like functions based on second order homogeneous kernels. First we prove the convergence of this new bundle interior proximal method under the same asumptions as for the standard bundle method and then we report some preliminary numerical experiences for a particular distance function.
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