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Tuomo Valkonen(tuomo.valkoneniki.fi) Abstract: We study the numerical solution of the problem $\min_{X \ge 0} \BXc\2$, 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 primaldual interior point method directly based on those for linear programs with semidefinite constraints, however not demanding the numerically expensive scalings inherent in these methods to force fast convergence. Keywords: semidefinite, interior point, projection, quadratic programming, diffusion tensor imaging. Category 1: Nonlinear Optimization (Quadratic Programming ) Category 2: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 3: Applications  Science and Engineering (Biomedical Applications ) Citation: T. Valkonen, A method for weighted projections to the positive definite cone, SFBReport 2012016, KarlFranzens University of Graz (2012). Download: [PDF] Entry Submitted: 08/06/2012 Modify/Update this entry  
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