2024/07/17 by Anton Klimza, Alexander Gasnikov, Klimza, Anton +5 · 1 citation
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2407.17519
openalex publication_date 2024/07/17 · openalex created_date 2024/09/19 · openalex updated_date 2026/07/28
In this paper, we propose universal proximal mirror methods to solve the variational inequality problem with Holder continuous operators in both deterministic and stochastic settings. The proposed methods automatically adapt not only to the oracle's noise (in the stochastic setting of the problem) but also to the Holder continuity of the operator without having prior knowledge of either the problem class or the nature of the operator information. We analyzed the proposed algorithms in both deterministic and stochastic settings and obtained estimates for the required number of iterations to achieve a given quality of a solution to the variational inequality. We showed that, without knowing the Holder exponent and Holder constant of the operators, the proposed algorithms have the least possible in the worst case sense complexity for the considered class of variational inequalities. We also compared the resulting stochastic algorithm with other popular optimizers for the task of image classification.