In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image … Read more
This paper concerns the method of selecting the best subset of explanatory variables in a multiple linear regression model. To evaluate a subset regression model, some goodness-of-fit measures, e.g., adjusted R^2, AIC and BIC, are generally employed. Although variable selection is usually handled via a stepwise regression method, the method does not always provide the … Read more
To handle significant variability in loads, renewable energy generation, as well as various contingencies, two-stage robust optimization method has been adopted to construct unit commitment models and to ensure reliable solutions. In this paper, we further explore and extend the modeling capacity of two-stage robust optimization and present two new robust unit commitment variants, the … Read more
Mixed Integer Nonlinear Programming (MINLP) techniques are increasingly used to address challenging problems in robotics, especially Multi-Vehicle Motion Planning (MVMP). The main contribution of this paper is a discrete time-distributed Receding Horizon Mixed Integer Nonlinear Programming (RH-MINLP) formulation of the underwater multi-vehicle path coordination problem with constraints on kinematics, dynamics, collision avoidance, and acoustic communication … Read more
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