A skeleton algorithm to solve linear programming problems and its applications for optimal estimation problems

Аuthors

Bakhshiyan B. T.¹, Goryainov A. V.²

1. Space Research Institute of the Russian Academy of Sciences , 84/32, Profsoyuznaya str, Moscow, 117997, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

Abstract

A new algorithm is proposed to solve ordinary and multiparameter (generalized) linear programming problems. The algorithm guarantees absence of almost degenerate iterations and does not require inversion of matrices. The algorithm was tested to solve optimal minimax estimation problems for polynomial and trigonometric models. Some examples are presented to demonstrate an effectiveness of the algorithm in comparison with the standard simplex method.