This paper establishes a direct method for solving variational problems via a set of Radial basis functions (RBFs) with Gauss-Chebyshev collocation centers. The method consist of reducing a variational problem into a mathematical programming problem. The authors use some optimization techniques to solve the reduced problem. Accuracy and stability of the multiquadric, Gaussian and inverse multiq...

In this paper, we study second-order optimality conditions for nonconvex set-constrained optimization problems. For a convex problem, it is well known that involve the support function of tangent set. propose two approaches establishing case. first approach, extend concept so applicable to general problems, whereas in second introduce notion directional regular cone and apply classical results ...

This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential equations arising from the model were discussed and existence and uniqueness were proved. Here, the focus is put on numerical methods: a monotone finite diff...

We consider the classical autonomous constrained variational problem of minimization of ∫ b a f(v(t), v ′(t))dt in the class Ω:={v ∈ W 1,1(a, b) : v(a) = α, v(b) = β, v′(t) ≥ 0 a.e. in (a, b)}, where f : [α, β] × [0,+∞) → R is a lower semicontinuous, nonnegative integrand, which can be nonsmooth, nonconvex and noncoercive. We prove a necessary and sufficient condition for the optimality of a tr...