Journal of convex analysis, Tome 12 (2005) no. 1, pp. 95-111
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N. T. T. Van; V. H. Nguyen; J.-J. Strodiot. A Bundle Interior Proximal Method for Solving Convex Minimization Problems. Journal of convex analysis, Tome 12 (2005) no. 1, pp. 95-111. http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a5/
@article{JCA_2005_12_1_JCA_2005_12_1_a5,
author = {N. T. T. Van and V. H. Nguyen and J.-J. Strodiot},
title = {A {Bundle} {Interior} {Proximal} {Method} for {Solving} {Convex} {Minimization} {Problems}},
journal = {Journal of convex analysis},
pages = {95--111},
year = {2005},
volume = {12},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a5/}
}
TY - JOUR
AU - N. T. T. Van
AU - V. H. Nguyen
AU - J.-J. Strodiot
TI - A Bundle Interior Proximal Method for Solving Convex Minimization Problems
JO - Journal of convex analysis
PY - 2005
SP - 95
EP - 111
VL - 12
IS - 1
UR - http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a5/
ID - JCA_2005_12_1_JCA_2005_12_1_a5
ER -
%0 Journal Article
%A N. T. T. Van
%A V. H. Nguyen
%A J.-J. Strodiot
%T A Bundle Interior Proximal Method for Solving Convex Minimization Problems
%J Journal of convex analysis
%D 2005
%P 95-111
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_2005_12_1_JCA_2005_12_1_a5/
%F JCA_2005_12_1_JCA_2005_12_1_a5
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.
