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math.OC2025
A Correspondence-Driven Approach for Bilevel Decision-making with Nonconvex Lower-Level Problems
Xiaotian Jiang, Jiaxiang Li, Jiawen Bi +2
We consider bilevel optimization problems with general nonconvex lower-level objectives and show that the classical hyperfunction-based formulation is unsettled, since the global m…
math.OC2025
A Note on the Convergence of Muon
Jiaxiang Li, Mingyi Hong
In this note, we inspect the convergence of a new optimizer for pretraining LLMs, namely the Muon optimizer. Such an optimizer is closely related to a specialized steepest descent…
math.OC2024
A Barrier Function Approach for Bilevel Optimization with Coupled Lower-Level Constraints: Formulation, Approximation and Algorithms
Xiaotian Jiang, Jiaxiang Li, Mingyi Hong +1
In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In…