We present an extension of convex-hull nonnegative matrix factorization (CH-NMF) which was recently proposed as a large scale variant of convex non-negative matrix factorization (CNMF) or Archetypal Analysis (AA). CH-NMF factorizes a non-negative data matrix V into two non-negative matrix factors V ≈ WH such that the columns of W are convex combinations of certain data points so that they are r...

In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.  

We develop a variant of multiclass logistic regression that achieves three properties: i) We minimize a non-convex surrogate loss which makes the method robust to outliers, ii) our method allows transitioning between non-convex and convex losses by the choice of the parameters, iii) the surrogate loss is Bayes consistent, even in the non-convex case. The algorithm has one weight vector per clas...

In this letter, we investigated the downlink transmission problem of a cognitive radio network (CRN) equipped with novel transmissive reconfigurable intelligent surface (TRIS) transmitter. order to achieve low power consumption and high-rate multi-streams communication, time-modulated arrays (TMA) is implemented users access using rate splitting multiple (RSMA). With such framework, multi-objec...

In this article we survey the existence of best proximity points for a class of non-self mappings which‎ satisfy a particular nonexpansiveness condition. In this way, we improve and extend a main result of Abkar and Gabeleh [‎A‎. ‎Abkar‎, ‎M‎. ‎Gabeleh‎, Best proximity points of non-self mappings‎, ‎Top‎, ‎21, (2013)‎, ‎287-295]‎ which guarantees the existence of best proximity points for nonex...

We study the online convex covering problem and online convex packing problem. The (offline) convex covering problem is modeled by the following convex program: min ~ x∈Rn+ f(~x) s.t. A~x ≥ ~1 where f : R+ 7→ R+ is a monotone and convex cost function, and A is an m × n matrix with non-negative entries. Each row of the constraint matrix A corresponds to a covering constraint. In the online probl...

an analytical equation of state is applied to calculate the thermodynamic properties for argon. theequation of state is that of song and mason. it is based on a statistical-mechanical perturbation theory ofhard convex bodies and can be written as fifth-order polynomial in the density. there exist three temperaturedependentparameters: the second virial coefficient, an effective molecular volume,...

This paper investigates a constrained formulation of neural networks where the output is convex function input. We show that convexity constraints can be enforced on both fully connected and convolutional layers, making them applicable to most architectures. The include restricting weights (for all but first layer) non-negative using non-decreasing activation function. Albeit simple, these have...

Given a quasi-concave-convex function f : X × Y → R defined on the product of two convex sets we would like to know if infY supX f = supX infY f . In [4] we showed that that question is very closely linked to the following “reconstruction” problem: given a polytope (i.e. the convex hull of a finite set of points) X and a family F of subpolytopes of X, we would like to know if X ∈ F, knowing tha...