Geodesic
A Proximal Extension of the Column Generation Method to Nonconvex Conic Optimization Providing Bounds for the Duality Gap
Journal of convex analysis, Tome 17 (2010) no. 3, pp. 721-736
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

We consider nonconvex conic optimization that covers Standard Nonlinear Programming, Semidefinite Programming, Second Order Cone Programming. To the dual Lagrangian problem, we associate a relaxed primal convex problem, and give bounds for the duality gap. Then we propose a proximal extension of the column generation method of Dantzig-Wolfe algorithm (PECGM) which provides these bounds if we suppose in addition Slater's condition. Finally new applications are given in order to make implementable the step of PECGM for which a nonconvex program is supposed to be solved numerically.
Mots-clés : Standard nonlinear programming, semidefinite programming, second order cone programming, duality gap, generation column algorithm, proximal method 
@article{JCA_2010_17_3_JCA_2010_17_3_a2,
     author = {A. Auslender},
     title = {A {Proximal} {Extension} of the {Column} {Generation} {Method} to {Nonconvex} {Conic} {Optimization} {Providing} {Bounds} for the {Duality} {Gap}},
     journal = {Journal of convex analysis},
     pages = {721--736},
     year = {2010},
     volume = {17},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a2/}
}
TY  - JOUR
AU  - A. Auslender
TI  - A Proximal Extension of the Column Generation Method to Nonconvex Conic Optimization Providing Bounds for the Duality Gap
JO  - Journal of convex analysis
PY  - 2010
SP  - 721
EP  - 736
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a2/
ID  - JCA_2010_17_3_JCA_2010_17_3_a2
ER  - 
%0 Journal Article
%A A. Auslender
%T A Proximal Extension of the Column Generation Method to Nonconvex Conic Optimization Providing Bounds for the Duality Gap
%J Journal of convex analysis
%D 2010
%P 721-736
%V 17
%N 3
%U http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a2/
%F JCA_2010_17_3_JCA_2010_17_3_a2
A. Auslender. A Proximal Extension of the Column Generation Method to Nonconvex Conic Optimization Providing Bounds for the Duality Gap. Journal of convex analysis, Tome 17 (2010) no. 3, pp. 721-736. http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a2/