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

作者：Auslender Alfred^*

来源：Journal of Convex Analysis, 2010, 17(3-4): 721-736.

• Standard nonlinear programming
• semidefinite programming
• second order cone programming
• duality gap
• generation column algorithm
• proximal method

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.

• 出版日期2010