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...

In this paper, we consider a streaming one-pass-over-the-data model for Principal Component Analysis (PCA). The input, in this case, is a stream of p-dimensional vectors, and the output is a collection of k, p-dimensional principal components that span the best approximating subspace. Consequently, the minimum memory requirement for such problems is O(kp). Yet the standard PCA algorithm require...

We consider streaming, one-pass principal component analysis (PCA), in the highdimensional regime, with limited memory. Here, p-dimensional samples are presented sequentially, and the goal is to produce the k-dimensional subspace that best approximates these points. Standard algorithms require O(p2) memory; meanwhile no algorithm can do better than O(kp) memory, since this is what the output it...

This paper studies a model of memory. The model takes into account that memory capacity is limited and imperfect. We study how agents with such memory limitations, who have very little information about their choice environment, play games. We introduce the notion of a Limited Memory Equilibrium (LME) and show that play converges to an LME in every generic normal form game. Our characterization...

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...

The BFGS method is one of the most famous quasi-Newton algorithms for unconstrained optimization. In 1984, Powell presented an example of a function of two variables that shows that the Polak–Ribière–Polyak (PRP) conjugate gradient method and the BFGS quasi-Newton method may cycle around eight nonstationary points if each line search picks a local minimum that provides a reduction in the object...

In this paper we present a modified BFGS algorithm for unconstrained optimization. The BFGS algorithm updates an approximate Hessian which satisfies the most recent quasi-Newton equation. The quasi-Newton condition can be interpreted as the interpolation condition that the gradient value of the local quadratic model matches that of the objective function at the previous iterate. Our modified al...

In this paper we present a new line search method known as the HBFGS method, which uses the search direction of the conjugate gradient method with the quasi-Newton updates. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) update is used as approximation of the Hessian for the methods. The new algorithm is compared with the BFGS method in terms of iteration counts and CPU-time. Our numerical analysis...