A Proximal Extension of the Column Generation Method to Nonconvex Conic Optimization Providing Bounds for the Duality Gap

被引：0
|
作者：
Auslender, Alfred [1 ,2 ]
机构：
[1] Univ Lyon 1, Inst Camille Jordan, F-69365 Lyon, France
[2] Ecole Polytech, Dept Econ, Palaiseau, France
来源：
JOURNAL OF CONVEX ANALYSIS | 2010年 / 17卷 / 3-4期
关键词：
Standard nonlinear programming; semidefinite programming; second order cone programming; duality gap; generation column algorithm; proximal method;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper 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.
引用
收藏
页码：721 / 736
页数：16
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