Jarre, Florian; Rendl, Franz An augmented primal-dual method for linear conic programs. (English) Zbl 1173.90497 SIAM J. Optim. 19, No. 2, 808-823 (2008). Summary: We propose a new iterative approach for solving linear programs over convex cones. Assuming that Slater’s condition is satisfied, the conic problem is transformed to the minimization of a convex differentiable function in the primal-dual space. This function shows similarities with the augmented Lagrangian function and is called “augmented primal-dual function” or “apd-function”. 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. Cited in 15 Documents MSC: 90C22 Semidefinite programming 90C25 Convex programming 49M29 Numerical methods involving duality Keywords:conic program; linear convergence; augmented primal-dual function Software:DIMACS; PENSDP; SDPLR PDFBibTeX XMLCite \textit{F. Jarre} and \textit{F. Rendl}, SIAM J. Optim. 19, No. 2, 808--823 (2008; Zbl 1173.90497) Full Text: DOI