The two dimensional bandwidth problem under the distances of L∞-norm and L1-norm has only been studied for a limited number of graphs. In this paper, I analyze the two dimensional bandwidth for a few different families of graphs.

L1 norm estimator has been widely used as a robust parameter estimation method for outlier detection. Different algorithms have been applied for L1 norm minimization among which the linear programming problem based on the simplex method is well known. In the present contribution, in order to solve an L1 norm minimization problem in a linear model, an interior point algorithm is developed which ...

This paper uses the L1−norm and the concept of the non-dominated vector, topropose a method to find a well-dispersed subset of non-dominated (WDSND) vectorsof a multi-objective mixed integer linear programming (MOMILP) problem.The proposed method generalizes the proposed approach by Tohidi and Razavyan[Tohidi G., S. Razavyan (2014), determining a well-dispersed subset of non-dominatedvectors of...

To date, little research on pragmatic transfer has considered a multilingual situation where there is an interaction among three different languages spoken by one person. Of interest was whether pragmatic transfer of refusals among three languages spoken by the same person occurs from L1 and L2 to L3, L1 to L2 and then to L3 or from L1 and L1 (if there are more than one L1) to L2. This study ai...

This lecture note describes an iterative optimization algorithm, ‘SALSA’, for solving L1-norm penalized least squares problems. We describe the use of SALSA for sparse signal representation and approximation, especially with overcomplete Parseval transforms. We also illustrate the use of SALSA to perform basis pursuit (BP), basis pursuit denoising (BPD), and morphological component analysis (MC...

The topic of this paper is the discrete-time l1-norm minimisation problem with convolution constraints. We find primal initial conditions for which the dual optimal solution is periodic. Periodicity of the dual optimal solution implies satisfaction of a simple linear recurrence relation by the primal optimal solution. c © 2007 Elsevier B.V. All rights reserved.

Linear subspace has many important applications in computer vision, such as structure from motion, motion estimation, layer extraction, object recognition, and object tracking. Singular Value Decomposition (SVD) algorithm is a standard technique to compute the subspace from the input data. The SVD algorithm, however, is sensitive to outliers as it uses L2 norm metric, and it can not handle miss...

We formalize an algorithm for solving the L(1)-norm best-fit hyperplane problem derived using first principles and geometric insights about L(1) projection and L(1) regression. The procedure follows from a new proof of global optimality and relies on the solution of a small number of linear programs. The procedure is implemented for validation and testing. This analysis of the L(1)-norm best-fi...