A well known theorem [3] in the theory of ordinary convex functions states that: A necessary and sufficient condition in order that the function be convex is that there is at least one line of support ...

The main result proved in this paper is that the ratio of the square of a nonnegative convex function to a strictly positive concave function is convex over a convex domain. Some particular cases of ...

We prove asymptotic normality of the new estimate and show that it is first order asymptotically equivalent to the initial unconstrained estimate if the regression function is in fact convex.

Discover the significance of the curvature of the marginal revenue product curve in microeconomic models. Explore how convex MRP curves are generated by renowned production functions.

This paper presents a novel recurrent neural network for solving nonlinear convex programming problems subject to nonlinear inequality constraints. Under the condition that the objective function is ...

Abstract: In this paper, we propose a successive convex approximation framework for sparse optimization where the nonsmooth regularization function in the objective function is nonconvex and it can be ...

We study the minimization problem of a non-convex sparsity promoting penalty function, the transformed \ (l_1\) (TL1), and its application in compressed sensing (CS).