Parameter-Free Non-Ergodic Extragradient Algorithms for Solving Monotone Variational Inequalities
Monotone variational inequalities (VIs) provide a unifying framework for convex minimization, equilibrium computation, and convex-concave saddle-point problems. Extragradient-type methods are among the most effective first-order algorithms for such problems, but their performance hinges critically on stepsize selection. While most existing theory focuses on ergodic averages of the iterates, practical performance is often driven by the significantly stronger behavior of the last iterate. Moreover, available last-iterate guarantees typically rely on fixed stepsizes chosen using problem-specific global smoothness information, which is often difficult to estimate accurately and may not even b...
| Authors | Lingqing Shen, Fatma Kılınç-Karzan |
|---|---|
| Primary category | math.OC |
| Published | 9 April 2026 |
| Last updated at source | 15 April 2026 |
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