Abstract

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 assumptions as for the standard bundle method and then we report some preliminary numerical experiences for a particular distance function

Author information

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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

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Suggested citation

N. T. T. Van, V. H. Nguyen, J.-J. Strodiot. “A Bundle Interior Proximal Method for Solving Convex Minimization Problems.” Journal of Convex Analysis 12 (2005), No. 1, 95–111. https://doi.org/10.68381/jca12006

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Published by Heldermann Verlag, 2005. Rights now held by Banach Press LLC.