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Optimization and Variational Analysis
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- When fractional quasi p-norms concentrate
Ivan Y. Tyukin, Bogdan Grechuk, Evgeny M. Mirkes, Alexander N. Gorban · 12 November 2025
Concentration of distances in high dimension is an important factor for the development and design of stable and reliable data analysis algorithms. In this paper, we address the fundamental long-standing question about the concentration of distances in high dimension for fractional quasi $p$-norms, …
- Solving bilevel optimization via sequential minimax optimization
Zhaosong Lu, Sanyou Mei · 11 November 2025
In this paper we propose a sequential minimax optimization (SMO) method for solving a class of constrained bilevel optimization problems in which the lower-level part is a possibly nonsmooth convex optimization problem, while the upper-level part is a possibly nonconvex optimization problem. Specifi…
- A Polynomial-Time Algorithm for Variational Inequalities under the Minty Condition
Ioannis Anagnostides, Gabriele Farina, Tuomas Sandholm, Brian Hu Zhang · 6 November 2025
Solving variational inequalities (SVIs) is a foundational problem at the heart of optimization. However, this expressivity comes at the cost of computational hardness. As a result, most research has focused on carving out specific subclasses that elude those intractability barriers. A classical prop…
- A Single-Loop First-Order Algorithm for Linearly Constrained Bilevel Optimization
Wei Shen, Jiawei Zhang, Minhui Huang, Cong Shen · 29 October 2025
We study bilevel optimization problems where the lower-level problems are strongly convex and have coupled linear constraints. To overcome the potential non-smoothness of the hyper-objective and the computational challenges associated with the Hessian matrix, we utilize penalty and augmented Lagrang…
- Problem-Parameter-Free Decentralized Bilevel Optimization
Zhiwei Zhai, Wenjing Yan, Ying-Jun Angela Zhang · 29 October 2025
Decentralized bilevel optimization has garnered significant attention due to its critical role in solving large-scale machine learning problems. However, existing methods often rely on prior knowledge of problem parameters-such as smoothness, convexity, or communication network topologies-to determi…