An Augmented Primal-Dual Method for Linear Conic Programs

We propose a new iterative approach for solving linear programs over convex cones. Assuming that Slaters condition is satisfied, the conic problem is transformed to the minimization of a convex differentiable function. This "agumented primal-dual function" or "apd-function" is restricted to an affine set in the primal-dual space. The evaluation of the function and its derivative is cheap if the projection of a given point onto the cone can be computed cheaply, and if the projection of a given point onto the affine subspace defining the primal problem can be computed cheaply. For the special case of a semidefinite program, a certain regularization of the apd-function is analyzed. Numerical examples minimizing the apd-function with a conjugate gradient method illustrate the potential of the approach. Key words. Conic program, linear convergence, augmented primal-dual function.

• Type: Journal
• Year: 2008
• Where: SIAMJO
• Authors: Florian Jarre, Franz Rendl
• Keywords: Conic Problem, Primal-dual Function, Primal-dual Space, SIAMJO 2008