Mathematical Design and Analysis of Iterative Methods for Linear and Nonlinear Problems
This talk presents a systematic approach to the design and analysis of iterative methods for solving linear and nonlinear problems.
Overview
We begin with auxiliary space theory, which offers a unified and conceptually simple framework for understanding a wide range of iterative methods for linear systems. The key idea is to interpret an iterative method for the original problem as an equivalent, more elementary method applied to an auxiliary problem posed on a larger space. Within this framework, the theory of subspace correction methods, encompassing many important algorithms such as domain decomposition and multigrid methods, can be derived in a natural way.
We then extend this perspective to nonlinear problems, with a particular focus on convex optimization. A framework of subspace correction methods for convex optimization and its various applications is introduced. Furthermore, we investigate close connections with other well-known classes of iterative schemes, including operator splitting and multiplier methods. The talk concludes with a discussion of emerging research directions inspired by this unified viewpoint, highlighting opportunities for new algorithmic developments, theoretical insights, and practical applications.
Presenters
Brief Biography
Jongho Park is a Research Scientist in the Applied Mathematics and Computational Sciences (AMCS) Program within the Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division at King Abdullah University of Science and Technology (KAUST), Saudi Arabia, where he works under the mentorship of Prof. Jinchao Xu. He received his B.S. degree in Mathematical Sciences and Computer Science in 2013, and his M.S. and Ph.D. degrees in Mathematical Sciences in 2015 and 2019, respectively, all from the Korea Advanced Institute of Science and Technology (KAIST), under the supervision of Prof. Chang-Ock Lee. From 2019 to 2020, he was a postdoctoral researcher in the Department of Mathematical Sciences at KAIST, mentored by Prof. Chang-Ock Lee. He then served as a Research Assistant Professor at the Natural Science Research Institute at KAIST from 2020 to 2023.
He has published more than 30 research articles, including papers in leading journals in computational mathematics. In 2024, he was a plenary speaker at the 28th International Conference on Domain Decomposition Methods, one of the premier international forums in the field. He was also a recipient of the 2020 S-Oil Award of Excellence for Doctoral Dissertation, which recognizes outstanding doctoral dissertations in the natural sciences in Korea.
