The l1-synthesis and l1-analysis models recover structured signals from their undersampled measurements. The solution of the former model is often a sparse sum of dictionary atoms, and that of the latter model often makes sparse correlations with dictionary atoms. This paper addresses the question: when can we trust these models to recover specific signals? We … Read more
The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields as e.g. in signal/image processing and statistics. A standard tool for dealing with sparse recovery is the ℓ1-regularized least-squares approach that has recently attracted the attention of many researchers. In this paper, we describe a new version … Read more
In this paper we consider a network with P nodes, where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector x* minimizing the sum of all the functions. We make the additional assumption that the functions have intersecting local domains, i.e., each function … Read more
We propose to use a decomposition of large-scale incremental four dimensional (4D-Var) data assimilation problems in order to make their numerical solution more efficient. This decomposition is based on exploiting an adaptive hierarchy of the observations. Starting with a low-cardinality set and the solution of its corresponding optimization problem, observations are adaptively added based on … Read more
We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a composition of a proper closed convex function P and a nonzero affine map, with the … Read more
We investigate constrained first order techniques for training Support Vector Machines (SVM) for online classification tasks. The methods exploit the structure of the SVM training problem and combine ideas of incremental gradient technique, gradient acceleration and successive simple calculations of Lagrange multipliers. Both primal and dual formulations are studied and compared. Experiments show that the … Read more
We investigate the control of constrained stochastic linear systems when faced with only limited information regarding the disturbance process, i.e. when only the first two moments of the disturbance distribution are known. We consider two types of distributionally robust constraints. The constraints of the first type are required to hold with a given probability for … Read more
We consider a problem of maximization of the distance traveled by a material point in the presence of a nonlinear friction under a bounded thrust and fuel expenditure. Using the maximum principle we obtain the form of optimal control and establish conditions under which it contains a singular subarc. This problem seems to be the … Read more
We propose a dynamic programming algorithm for projection onto wavelet tree structures. In contrast to other recently proposed algorithms which only give approximate tree projections for a given sparsity, our algorithm is guaranteed to calculate the projection exactly. We also prove that our algorithm has O(Nk) complexity, where N is the signal dimension and k … Read more
A new algorithm for the solution of multimaterial topology optimization problems is introduced in the present study. The presented method is based on the splitting of a multiphase topology optimization problem into a series of binary phase topology optimization sub-problems which are solved partially, in a sequential manner, using a traditional binary phase topology optimization … Read more