Stability principles and approximation problems in variational calculus - P. Kosmol; Muller-Wichards, D. (Հայաստանի ԳԱԱ)
The problem of pointwise minimization of the Langrangian is approached by a simultaneeous optimization with respect to both state and control variables. The Legendre-Riccati condition ensures the existence of an equivalent convex variational problem, making possible application of the corresponding stability principles. The approach also provides an elementary acess to the fundamental theorems of variational calculus, without employing the theory of fields of extremals. Applications are in the problems of modular and parameter-free approximation of time-series data by monotone functions. We present a method, based on variational calculus, to determine a smooth monotone function that approximates a given time-series data in the least squares sense.
Keywords: Mathematics; Science