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Stream: Large scale optimization

Chair: Stephen Wright

1. A two-stage active-set method for bound-constrained optimization problems
   Andrea Cristofari, Marianna De Santis, Stefano Lucidi, Francesco Rinaldi
   
   
   

   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.
   
   

2. Preconditioners for inexact Newton method in big data optimization
   Jacek Gondzio
   
   
   

   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.
   
   

3. Ordering in Gauss-Seidel Iterations
   Weiqi Zhou
   
   
   

   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.
   
   

4. CANCELED
   smartDESC: Demand Response via Electric Water Heaters to Support the Integration of Intermittent Power Generation in a Smart Grid
   Miguel Anjos
   
   
   
5. Some Optimization Problems from Electrial Power Grids
   Stephen Wright, Taedong Kim, Taedong Kim
   
   
   

   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