mathnasТруды Института математики НАН БеларусиProceedings of the Institute of Mathematics of the NAS of Belarus1812-5093Институт математики НАН Беларусиmathnas-43Research ArticleДИСКРЕТНАЯ МАТЕМАТИКА И МАТЕМАТИЧЕСКАЯ КИБЕРНЕТИКАDISCRETE MATHEMATICS AND MATHEMATICAL CYBERNETICSНевыступающие фасады конуса полностью положительных матрицNon-exposed faces of the cone of completely positive matricesКостюковаО. И.KostyukovaO. I.

Минск

Minsk

kostyukova@im-bas-net.byИнститут математики НАН БеларусиInstitute of Mathematics of the National Academy of Sciences of Belarus,2024030320253225668Copyright © Костюкова О.И., 20252025Костюкова О.И.Kostyukova O.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://mathnas.ejournal.by/jour/article/view/43

В данной работе мы рассматриваем конус полностью положительных матриц. К настоящему время в литературе были построены некоторые семейства невыступающих полиэдральных фасадов этого конуса. Мотивированные этими результатами, в данной работе мы продолжаем изучение свойств невыступающих фасадов конуса полностью положительных матриц. Доказаны условия, выполнение которых необходимо и достаточно для того, чтобы фасад этого конуса был невыступающим. Также получены достаточные условия, которые можно легко проверить численно. Показано, что для любого $p\geqslant 6$ существуют невыступающие неполиэдральные фасады конуса $p\times p$ полностью положительных матриц. Приведены иллюстративные примеры

In this paper, we consider the cone of completely positive matrices. Currently, some families of non-exposed polyhedral faces of this cone were constructed. Inspired by these results, in this paper, we continue the study of the existence and properties of non-exposed faces of the cone of completely positive matrices. We prove a criterion for a face of this cone to be non-exposed. We also provide sufficient conditions that can be easily checked numerically. We show that for any $p\geqslant 6$, there exist non-exposed non-polyhedral faces of the cone of $p\times p$ completely positive matrices. Illustrative examples are given

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The authors declare that there are no conflicts of interest present.