Sparse optimization is a research hotspot in operations research optimization, with extensive applications in fields such as information theory, image science, and machine learning; Non convex sparse optimization methods exhibit strong sparsity reduction and noise robustness in applications. The study of gene regulatory networks is an important tool for biomedical research, which explains the phenomena of life and evolution through the interactions between genes. This report will introduce the bridge between sparse optimization and gene regulatory networks, and describe the non convex sparse optimization models corresponding to various gene regulatory network structures. We will also focus on introducing the mathematical theory of non convex sparse optimization models, including the theory of model consistency and asymptotic behavior, equivalent characterization of optimal solutions, linear convergence rate and global convergence theory of first-order algorithms, etc.
Reporter's profile: Hu Yaohua obtained his bachelor's and master's degrees from Zhejiang University, and his doctoral degree from the Hong Kong Polytechnic University. I am currently a Distinguished Professor, Vice Dean, and Doctoral Supervisor at the School of Mathematical Sciences, Shenzhen University. I am also a part-time doctoral supervisor at the Hong Kong Polytechnic University and a Youth Director of the Mathematical Planning Branch of the China Operations Research Society. I am also a member of the Science Popularization Committee of the China Operations Research Society. Mainly engaged in continuous optimization theory, methods, and application research, representative achievements have been published in well-known journals such as SIAM Journal on Optimization, Inverse Problems, Journal of Machine Learning Research, etc., authorized 3 national invention patents, developed multiple bioinformatics toolkits, and has led more than 10 national and provincial level scientific research projects, including the National Natural Science Foundation of China's Excellent Youth Science Fund.
