@online{Kamkari_2111.02291,
TITLE = {Physarum Inspired Dynamics to Solve Semi-Definite Programs},
AUTHOR = {Gao, Yuan and Kamkari, Hamidreza and Karrenbauer, Andreas and Mehlhorn, Kurt and Sharifi, Mohammadamin},
LANGUAGE = {eng},
URL = {https://arxiv.org/abs/2111.02291},
EPRINT = {2111.02291},
EPRINTTYPE = {arXiv},
YEAR = {2022},
ABSTRACT = {Physarum Polycephalum is a Slime mold that can solve the shortest path<br>problem. A mathematical model based on the Physarum's behavior, known as the<br>Physarum Directed Dynamics, can solve positive linear programs. In this paper,<br>we will propose a Physarum based dynamic based on the previous work and<br>introduce a new way to solve positive Semi-Definite Programming (SDP) problems,<br>which are more general than positive linear programs. Empirical results suggest<br>that this extension of the dynamic can solve the positive SDP showing that the<br>nature-inspired algorithm can solve one of the hardest problems in the<br>polynomial domain. In this work, we will formulate an accurate algorithm to<br>solve positive and some non-negative SDPs and formally prove some key<br>characteristics of this solver thus inspiring future work to try and refine<br>this method.<br>},
}