We show that a PL-realization of a closed connected manifold of dimension n − 1 in R (n ≥ 3) is the boundary of a convex polyhedron if and only if the interior of each (n− 3)-face has a point, which has a neighborhood lying on the boundary of a convex n-dimensional body. This result is derived from a generalization of Van Heijenoort’s theorem on locally convex manifolds to the spherical case. N...

Our aim in this paper is to present a reduction method that solves first order functional differential inclusion the nonconvex case. This approach based on discretization of time interval, construction approximate solutions by reducing problem without delay and an application known results We generalises earlier results, right hand side has values satisfies linear growth condition instead be in...

We consider the revenue management problem of finding profit-maximizing prices for delivery time slots in context attended home delivery. This multistage optimal control admits a dynamic programming (DP) formulation that is intractable realistic sizes due to so-called “curse dimensionality.” therefore study three approximate DP algorithms both from numerical and control-theoretical perspective....

The aim of this paper is to find a convenient and practical method to approximate a given real-valued function of multiple variables by linear operators, which approximate all strongly convex functions from above (or from below). Our main contribution is to use this additional knowledge to derive sharp error estimates for continuously differentiable functions with Lipschitz continuous gradients...

Throughout, X stands for a real Banach space, SX for its unit sphere, X ∗ for its topological dual, and 〈·, ·〉 for the duality pairing. All the functions f : X → R∪{+∞} are lower semicontinuous. The Clarke subdifferential , the Hadamard subdifferential and the Fréchet subdifferential of f are respectively denoted by ∂Cf , ∂Hf and ∂F f . The Zagrodny two points mean value inequality has proved t...

An interesting property of the midpoint rule and trapezoidal rule, which is expressed by the so-called Hermite–Hadamard inequalities, is that they provide one-sided approximations to the integral of a convex function. We establish multivariate analogues of the Hermite–Hadamard inequalities and obtain access to multivariate integration formulae via convexity, in analogy to the univariate case. I...