A method for weighted projections to the positive definite cone

We study the numerical solution of the problem minX≥0 ‖BX−c‖2, where X ∈ Sm is a symmetric square matrix, and B : Sm → R is a linear operator, such that B∗B is invertible. With ρ the desired fractional duality gap, we prove O( √ m log ρ−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. Mathematics subject classification: 90C22, 90C51, 92C55.