List of issues > Series «Mathematics». 2011. Vol. 2
Linear inequalities system’s solutions least distant from origin of coordinates
The problem of searching the least distant point of polyhedron from origin of coordinates in several statements is considered. A polyhedron is defined as a solution set of system of linear inequalities. Also the results of solving penalty functions minimizations problems including Holder norms with different power and weighting coefficients are considered. The multicriterion problem of searching vector of solutions of system of inequalitues with Pareto-minimal absolute values of all components is discussed. Theorems about relationship of sets of solutions of different statements of problem under consideration are formulated and proved.
1. Багратуни Г. В. Предисловие / Г. В. Багратуни // Избранные геофизические сочинения / К. Ф. Гацес. – М. : Геодезист, 1967.
2. Зоркальцев В. И. Метод наименьших квадратов: геометрические свойства, альтернативные подходы, приложения / В. И. Зоркальцев. – Новосибирск : Наука, 1995. – 270 с.
3. Линник Ю. В. Метод наименьших квадратов и основы математико-статистической теории обработки наблюдений / Ю. В. Линник. – М. : Физматгиз, 1962. – 349 с.
4. Лоусон Ч. Численное решение задач метода наименьших квадратов / Ч. Лоусон, Р. Хенсон. – М. : Наука, 1986. – 232 с.