ON SOME GENERALIZATION OF SMOOTHING PROBLEMS

The paper deals with the generalized smoothing problem in abstract Hilbert spaces. This generalized problem involves particular cases such as the interpolating problem, the smoothing problem with weights, the smoothing problem with obstacles, the problem on splines in convex sets and others. The theorem on the existence and characterization of a solution of the generalized problem is proved. It is shown how the theorem gives already known theorems in special cases as well as some new results.

Splines in convex sets under constraints of two‐sided inequality type in a hyperplane

The problem of minimization of a smoothing functional under inequality constraints is considered in a hyperplane. The conditions of the existence of a solution are obtained and some properties of this solution are investigated. It is proved that the solution is a spline. The method for its construction is suggested. First Published Online: 14 Oct 2010

Adaptation of course of operations research to needs of engineering study programmes by including specific models and examples

On usage of visualization tools in teaching mathematics at universities

Optimal Control Under Fuzzy Conditions for Dynamical Systems Associated with the Second Order Linear Differential Equations

This paper is devoted to an optimal trajectory planning problem with uncertainty in location conditions considered as a problem of constrained optimal control for dynamical systems. Fuzzy numbers are used to incorporate uncertainty of constraints into the classical setting of the problem under consideration. The proposed approach applied to dynamical systems associated with the second order linear differential equations allows to find an optimal control law at each \(\alpha \)-level using spline-based methods developed in the framework of the theory of splines in convex sets. The solution technique is illustrated by numerical examples.