Structured Bilevel and Multilevel Optimization for Complex Decision-Making

Bilevel and multilevel optimization is increasingly relevant to scientific, engineering, and data-driven settings in which decisions are naturally hierarchical, sequential, or interdependent. Applications span machine learning, hyperparameter and model selection, inverse problems, signal processing, engineering design, resource allocation, planning, and decision-support systems. However, many contemporary problems also involve nonconvexity, nonsmooth regularization, sparsity, low-rank constraints, uncertainty, and large-scale data, creating challenges in solution characterization, convergence analysis, scalability, robustness, and the coordination of multiple decision levels. Recent developments in first-order, proximal, gradient-based, stochastic, derivative-free, and structure-exploiting methods are broadening the range of hierarchical problems that can be addressed, although important theoretical and computational gaps remain.This Research Topic aims to advance the theory, algorithms, and applications of structured bilevel and multilevel optimization for complex decision-making. It will address questions concerning the formulation and characterization of hierarchical optimization problems, the design of reliable and computationally efficient algorithms, and the analysis of convergence, complexity, stability, and robustness under realistic structural conditions. Particular emphasis will be placed on methods that exploit sparsity, low-rank structure, problem geometry, data characteristics, or uncertainty. The Research Topic also seeks to strengthen connections between optimization theory and decision-oriented applications by identifying approaches that can translate complex hierarchical processes into practical and actionable computational frameworks.To gather further insights in structured bilevel and multilevel optimization for complex decision-making, we welcome articles addressing, but not limited to, the following themes:- Nonconvex and nonsmooth bilevel and multilevel optimization- First-order, gradient-based, proximal, stochastic, and derivative-free algorithms- Convergence, complexity, stability, and sensitivity analysis- Structure-exploiting methods for sparse, low-rank, matrix, and tensor optimization- Hyperparameter optimization and model selection- Machine learning and data-driven hierarchical optimization- Inverse problems and signal processing- Optimization under uncertainty and robust hierarchical decision-making- Large-scale and distributed computational methods- Engineering design, planning, resource allocation, and decision-support applications- Mathematical modelling of complex hierarchical decision processesOriginal Research, Methods, Review, and Perspective articles addressing these themes are welcome. Topic editors: Laura Selicato, Flavia Esposito Source: https://www.frontiersin.org/research-topics/85772/structured-bilevel-and-multilevel-optimization-for-complex-decision-making