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A method for weighted projections to the positive definite cone

Tuomo Valkonen(tuomo.valkonen***at***iki.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: 08/06/2012
Entry Accepted: 08/06/2012
Entry Last Modified: 08/06/2012

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