Accelerated diagonal gradient-type method for large-scale unconstrained optimization
In this study, we propose an accelerated diagonal-updating scheme for solving large-scale optimization, where a scaled diagonal matrix is used to approximate the Hessian. We combine an accelerator with the diagonal-updating method to improve the efficiency of the algorithm. This accelerator is employed to ensure that the function value can be reduced significantly at each step. Moreover, the algorithm employs a suitable monotone strategy to guarantee the global convergence of the algorithm. Several numerical results are reported, which demonstrate that the proposed method is promising and more robust than other diagonal updating schemes.
Jointly Gaussian memoryless sources are observed at N distinct terminals. The goal is to efficiently encode the observations in a distributed fashion so as to enable reconstruction of any one of the observations, say the first one, at the decoder subject to a quadratic fidelity criterion. Our main result is a precise characterization of the rate-distortion region when the covariance matrix of the sources satisfies a ?tree-structure? condition. In this situation, a natural analog-digital separation scheme optimally trades off the distributed quantization rate tuples and the distortion in the reconstruction: each encoder consists of a point-to-point Gaussian vector quantizer followed by a Slepian-Wolf binning encoder. We also provide a partial converse that suggests that the tree-structure condition is fundamental.