# A method for weighted projections to the positive definite cone

We study the numerical solution of the problem $\min_{X \ge 0} \|BX-c\|2$, where $X$ is a symmetric square matrix, and $B$ a linear operator, such that $B^*B$ is invertible. With $\rho$ the desired fractional duality gap, we prove $O(\sqrt{m}\log\rho^{-1})$ iteration complexity for a simple primal-dual interior point method directly based on those for linear programs with semi-definite constraints, however not demanding the numerically expensive scalings inherent in these methods to force fast convergence.

## Citation

T. Valkonen, A method for weighted projections to the positive definite cone, SFB-Report 2012-016, Karl-Franzens University of Graz (2012).