We discuss a general technique that forms a differentiable bound on non-differentiable objective functions by bounding the function optimum by its expectation with respect to a parametric variational distribution. We describe sufficient conditions for the bound to be convex with respect to the variational parameters. As example applications we consider variants of sparse linear regression and S...

A special class of differentiable functions on an infinite integral domain which is not a field is introduced. Some facts about these functions are established and the special case of z is studied in more detail

The paper studies the unmeasurable disturbance decoupling problem via the dynamic output feedback for discrete-time nonlinear control systems. To address the problem the novel algebraic approach, called the algebra of functions, is applied. The advantage of the latter over the differential geometric methods is that the system description may depend on non-differentiable functions.

We study the Lp-approximation problem (1 ≤ p < ∞) for infinitely differentiable d-variate functions with respect to the worst case error. In particular, we correct a mistake in the argumentation of Novak and Woźniakowski [2], who showed that the problem is intractable. The main ingredients are arguments from convex geometry, as well as a probabilistic calculation.

the purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of sturm-liouville problem with equation of the form w??=(?2f(x)?r(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in c2(a,b which has a single zero (so called turning point) at point 0x=x and r(x) is a continuously differentiable function. ...

The Cauchy–Nicoletti boundary value problem for a system of ordinary differential equations with pole-type singularities is investigated. The conditions of the existence, uniqueness, and nonuniqueness of a solution in the class of continuously differentiable functions are given. The classical Banach contraction principle is combined with a special transformation of the original problem. Introdu...

Hub-and-spoke (HS) network designs arise in transportation and telecommunications systems, where items must flow among spatially separate nodes and scale economies can be attained through the shared use of high capacity links between hubs. As an alternative for the discrete approach of selecting a subset of the existing nodes as hubs, this paper explores the possibility of their continuous loca...