MSC: 90C26, 93D09, 15A18
DOI: 10.21538/0134-4889-2026-32-3-85-95
In this paper we consider the minimization problem for a continuous function which is written as a maximum of a family of Lipschitz functions. The sequence of auxiliary minimization problems is introduced, where the objective functions of the auxiliary problem consist of finite pointwise maxima. The applications to some eigenvalue minimization problems, such as common Lyapunov functions and stable member of a matrix polytope, are considered.
Keywords: Minimax, nonlinear programming, common Lyapunov function, stable member
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Received May 14, 2026
Revised May 18, 2026
Accepted May 18, 2026
Vakif Dzhafarov, Dr., Prof., Department of Mathematics, Faculty of Science, Eskisehir Technical University, Eskişehir, Turkey, e-mail: vcaferov@eskisehir.edu.tr
İpek Cafer Ismayilov, Department of Mathematics, Faculty of Science, Marmara University, İstanbul, Turkey, e-mail: ipek.ismayilov@marmara.edu.tr
Taner Büyükköroğlu, Dr., Prof., Department of Mathematics, Faculty of Science, Eskisehir Technical University, Eskişehir, Turkey, e-mail: tbuyukkoroglu@eskisehir.edu.tr
Cite this article as: V. Dzhafarov, İ.C. Ismayilov, T. Büyükköroğlu. Nonsmooth minimization with applications to some eigenvalue problems. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol 32, no. 3, pp. 85–95.
Русский
В. Джафаров, И.Дж. Исмаилов, Т. Бююккороглу. Негладкая минимизация и ее приложения к некоторым задачам на собственные значения
В данной работе рассматривается задача минимизации непрерывной функции, представимой в виде максимума семейства липшицевых функций. Вводится последовательность вспомогательных задач минимизации, в которых целевые функции имеют вид конечных поточечных максимумов. Рассматриваются приложения к задачам минимизации собственных значений, таким как построение общих функций Ляпунова и нахождение устойчивого элемента в матричном политопе.
Ключевые слова: минимакс, нелинейное программирование, общая функция Ляпунова, устойчивый элемент
