In this paper we proposed quasi-Newton and limited memory quasi-Newton methods for objective functions defined on Grassmann manifolds or a product of Grassmann manifolds. Specifically we defined bfgs and l-bfgs updates in local and global coordinates on Grassmann manifolds or a product of these. We proved that, when local coordinates are used, our bfgs updates on Grassmann manifolds share the s...

The predominant methodology in training deep learning advocates the use of stochastic gradient descent methods (SGDs). Despite its ease of implementation, SGDs are difficult to tune and parallelize. These problems make it challenging to develop, debug and scale up deep learning algorithms with SGDs. In this paper, we show that more sophisticated off-the-shelf optimization methods such as Limite...

Linear minimum mean square error (MMSE) detection achieves a good trade-off between performance and complexity for massive multiple-input multiple-output (MIMO) systems. To avoid the high-dimensional matrix inversion involved, MMSE can be transformed into an unconstrained optimization problem then solved by efficient numerical algorithms in iterative way. Three low-complexity Broyden-Fletcher-G...

A MATLAB implementation of the Moré-Sorensen sequential (MSS) method is presented. The MSS method computes the minimizer of a quadratic function defined by a limited-memory BFGS matrix subject to a two-norm trust-region constraint. This solver is an adaptation of the Moré-Sorensen direct method into an L-BFGS setting for large-scale optimization. The MSS method makes use of a recently proposed ...

This paper proposes a modified BFGS formula using a trust region model for solving nonsmooth convex minimizations by using the Moreau-Yosida regularization (smoothing) approach and a new secant equation with a BFGS update formula. Our algorithm uses the function value information and gradient value information to compute the Hessian. The Hessian matrix is updated by the BFGS formula rather than...