Optimization of spline parameters in approximation of multivalued functions

Objectives. Methods for spline approximation of a sequence points in plane are increasingly used various disciplines. A is defined as single-valued function consisting known number repeating elements, which the most widely polynomials. When designing routes linear structures, it necessary to consider problem with an unknown elements. An algorithm implemented solving this when longitudinal profile was published earlier. Here, since elements comprise circular arcs conjugated by line segments, function. However, route plan, generally multivalued Therefore, previously developed unsuitable problem, even if same used. The aim work generalize obtained results case functions while considering features involved structures. first stage consisted determining approximating using dynamic programming. In present paper, next carried out. Methods. parameters were optimized new mathematical model form modified Lagrange and special nonlinear programming algorithm. case, possible analytically calculate derivatives objective respect absence its analytical expression. Results. optimize segments. initial at stage. Conclusions. proposed two-stage scheme also suitable given plane, particular, plan