Bridging Optimization Theory and Numerical Analysis: New Developments for Nonconvex and Nonsmooth Problems

Reference No.	2026a011
Type/Category	Grant for Young Researchers and Students-Short-term Joint Research
Title of Research Project	Bridging Optimization Theory and Numerical Analysis: New Developments for Nonconvex and Nonsmooth Problems
Principal Investigator	Jiabao Yang（Musashino University・First-year Ph.D. student）
Research Period	August 6,2026. - August 8,2026.
Keyword(s) of Research Fields	Numerical Analysis, Nonconvex Optimization, Convex Optimization, Nonlinear Optimization, and Unconstrained Optimization
Abstract for Research Report	This study aims to develop a novel theoretical framework that integrates optimization theory and numerical analysis to address “nonconvex and nonsmooth optimization problems,” which frequently arise in data analysis associated with real-world challenges, and to design algorithms with a view toward practical implementation. Rather than serving merely as a platform for information exchange, this project fully exploits the scheme of a “short-term collaborative research program.” Throughout the research period, experts from diverse fields will engage in intensive discussions from multiple perspectives, while small-scale workshops will be organized to promote broad information exchange and to foster the initiation of new collaborative research. The specific research topics include addressing stagnation at local minima and slow convergence in deep learning and related areas. In particular, we aim to refine convergence analysis based on the Kurdyka–Łojasiewicz (KL) inequality and to establish theoretical guarantees for convergence in nonconvex extensions of optimization methods such as the proximal gradient method. In parallel, we will apply techniques from numerical analysis to nonsmooth systems to design efficient search algorithms. Building upon these theoretical advances, and recognizing that optimization technologies form a fundamental basis for solving societal challenges, we will pursue application-oriented studies. These include high-precision reconstruction in medical image processing (e.g., MRI), robustification of machine learning models against noisy data, and optimization of complex supply chains. Through these applications, we seek to demonstrate the practical effectiveness of the proposed methods. During the research meetings, invited speakers and collaborators will engage in intensive joint work and discussions aligned with the objectives of the short-term collaborative research program. This collaborative effort is expected to contribute both to the advancement of optimization theory and to the enhancement of computational techniques for real-world applications.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Jiabao Yang（Musashino University・First-year Ph.D. student） Takiko Sasaki（Musashino University・Associate Professor） Shun Sato（Tokyo Metropolitan University・Associate Professor） Naoki Marumo（NTT Communication Science Laboratories, The University of Tokyo・Assistant Professor (Specially Appointed)）