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

Abstract

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.

Key words:

• smoothing problem
• spline
• simplex method