- A method for weighted projections to the positive definite cone Tuomo Valkonen(tuomo.valkoneniki.fi) Abstract: 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. Keywords: semi-definite, interior point, projection, quadratic programming, diffusion tensor imaging. Category 1: Nonlinear Optimization (Quadratic Programming ) Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming ) Category 3: Applications -- Science and Engineering (Biomedical Applications ) Citation: T. Valkonen, A method for weighted projections to the positive definite cone, SFB-Report 2012-016, Karl-Franzens University of Graz (2012). Download: [PDF]Entry Submitted: 08/06/2012Entry Accepted: 08/06/2012Entry Last Modified: 08/06/2012Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.