Saturday, 11:10 - 12:50 - Room 161
Stream: Large scale optimization
We propose a two-stage active-set method for large scale problems with bound constraints. At each iteration, in the first stage we estimate the active variables and fix them to the bounds, and in the second stage we perform a line search along a projected truncated-Newton direction computed in the subset of the estimated non-active variables.
The proposed algorithm embeds these two stages within a nonmonotone stabilization framework. Global convergence to stationary points is established. Promising results were obtained on some bound-constrained problems from the CUTEst collection.
We address efficient preconditioning techniques for the second-order methods applied to solve various sparse approximation problems arising in big data optimization. The preconditioners cleverly exploit special features of such problems and cluster the spectrum of eigenvalues around one. The inexact Newton Conjugate Gradient method excels in these conditions. Numerical results of solving L1-regularization problems of unprecedented sizes reaching a trillion of variables will be presented.
This is a joint work with Kimonas Fountoulakis.
The Gauss-Seidel iterative method is a classical way of solving linear systems with positive (semi-)definite matrices. One of its equivalent form, known as the Kaczmarz method, is still widely used in CT/signal processing.
It is often observed that ordering of the equations plays a vital role for this method. We gave an explanation on why given equation orderings are often sub-optimal and how does reordering helps to improve the situation on average. These are based on understanding the spectral properties of the triangular truncation, which is an analogous operator of the Riesz projection.
We describe several problems in optimization and data analysis arising from electrical power grids. First, we formulate a bilevel optimization problem to identify possible vulnerabilities by finding the attack that causes maximal disruption. Second, we describe a multivariate logistic regression (MLR) approach for identifying outages in a grid from real-time sensor network data. We show that when the MLR classifier is trained to recognize the "signature" of outages under a variety of network conditions, it can identify outages correctly in the vast majority of cases. An ex