On continuous functions with no unilateral derivatives

Necessary Conditions without Differentiability Assumptions in Unilateral Control Problems*

We derive two theorems combining existence with necessary conditions for the relaxed unilateral problem of the optimal control of ordinary differential equations in which the functions that define the problem are Lipschitz-continuous in the state variables. These theorems generalize the results presented in a previous paper [8] by the addition of unilateral constraints on the state and control ...

Rings of functions with integer derivatives at x=1

Continuous Discrete Variable Optimization of Structures Using Approximation Methods

Optimum design of structures is achieved while the design variables are continuous and discrete. To reduce the computational work involved in the optimization process, all the functions that are expensive to evaluate, are approximated. To approximate these functions, a semi quadratic function is employed. Only the diagonal terms of the Hessian matrix are used and these elements are estimated fr...

On images of continuous functions from a compact manifold to Euclidean space

The Space of Density Continuous Functions

A function f : R → R is density continuous if it is continuous when using the density topology on both its domain and range. The set of density continuous functions contains all convex functions and all real analytic functions, but does not contain all C∞ functions. It is not closed under addition. We denote by Rd the set of real numbers, R, endowed with the density topology. A function f : Rd ...