We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS. Thereafter, non-asymptotic high-probability bounds are established on the e...

A space X is truly weakly pseudocompact if X is either weakly pseudocompact or Lindelöf locally compact. We prove: (1) every locally weakly pseudocompact space is truly weakly pseudocompact if it is either a generalized linearly ordered space, or a protometrizable zero-dimensional space with χ(x,X) > ω for every x ∈ X; (2) every locally bounded space is truly weakly pseudocompact; (3) for ω < κ...

The symmetric regularized long wave system (SRLW) is a model for weakly nonlinear ion acoustic and space-charge waves, introduced by C. Seyler D. Fenstermacher. In this paper, we investigate the Wellposedness controllability properties of generalized (g-SRLW) in different structures, such as periodic bounded domains. Firstly, obtain exact results both linear g-SRLW posed on one-dimensional toru...

A graph is triangulated if it has no chordless cycle with at least four vertices (8k 4; C k 6 6 G). These graphs have been generalized by R. Hayward with the weakly triangulated graphs (8k 5; C k ; C k 6 6 G). In this note we propose a new generalization of triangulated graphs. A graph G is slightly triangulated if it satisses the two following conditions : 1. G contains no chordless cycle with...

We consider an algorithm that successively samples and minimizes stochastic models of the objective function. We show that under weak-convexity and Lipschitz conditions, the algorithm drives the expected norm of the gradient of the Moreau envelope to zero at the rate O(k−1/4). Our result yields the first complexity guarantees for the stochastic proximal point algorithm on weakly convex problems...

A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may define a generalized, Tsallis type dynamical entropy that increases linearly with time. It characterizes a maximal gain of information about the system that incre...

The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy contra weakly generalized continuous mappings in intuitionistic fuzzy topological space. Some of their properties are explored. 2010 AMS Classification: 54A40, 03E72