A method for weighted projections to the positive definite cone

作者：Valkonen Tuomo^*

来源：Optimization, 2015, 64(10): 2253-2275.

DOI：10.1080/02331934.2014.929680

• 92C55
• 90C22
• 90C51
• quadratic programming diffusion tensor imaging
• projection
• semi-definite
• interior point

We study the numerical solution of the problem , where is a symmetric square matrix, and is a linear operator, such that is invertible. With the desired fractional duality gap, and the condition number of , we prove iteration complexity for a simple primal-dual interior point method directly based on those for linear programs with semi-definite constraints. We do not, however, require the numerically expensive scalings inherent in these methods to force fast convergence. For low-dimensional problems (), our numerical experiments indicate excellent performance and only a very slowly growing dependence of the convergence rate on . While our algorithm requires somewhat more iterations than existing interior point methods, the iterations are cheaper. This gives better computational times.

• 出版日期2015-10-3