ProbXiv
sign in
unchecked

pth-Order Oracle Complexity for Monotone Variational Inequalities

Nothing has been published against this problem here, and nobody has checked anything. That is the ordinary condition of an open problem, not a defect in the record.

monotone-vi-pth-order-complexityAlgorithms & optimizationposed by Renato D. C. Monteiro, Benar F. Svaiter, 2012recorded: solved

1 attempt · no person has looked

Statement

Monteiro and Svaiter gave a second-order method for smooth monotone variational inequalities converging at O(T^-1.5), later improved to O(T^-1.75) for the convex-concave minimax subset. Whether the conjectured complexity for general monotone variational inequalities could be improved was open. A large-step inexact Halpern iteration achieves O(T^-2), and O(T^-p) at pth order.

Context

Improves every prior result for p >= 2 and matches the classical extragradient method at p = 1.

An explicitly stated open question in the higher-order-methods literature, resting on a well-cited Monteiro-Svaiter framework but confined to optimization theory.

People

no project yet · nobody looking

Projects

none yet

Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.

begin a project on this problem →

Interest

nobody looking

Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.

Attempts

1 attempt

No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

review this attempt →

  • #1

    Attempt 1

    proof attemptClaude Opus 4.6 and GPT-5.6 Sol with Lesi Chen, Xinliang Zhang, Hengyu Wang, Chengchang Liu, Yongchao Chen, Jingzhao Zhang ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    Claude Opus 4.6 and GPT-5.6 Sol
    people
    Lesi Chen, Xinliang Zhang, Hengyu Wang, Chengchang Liu, Yongchao Chen, Jingzhao Zhang

    The paper records the sequence: an O(T^-(p-1)) rate was obtained with Claude Opus 4.6, and on verifying it the authors conjectured a better O(T^-p) result, for which Xinliang Zhang then found a proof with GPT-5.6 Sol. The results were subsequently verified by the human authors, who also link the model's initial proof as a public ChatGPT transcript.

    Reviews

    0 human reviews · 0 machine checks

    No person has reviewed this attempt. It has not been checked at all.

    Endorsements

    0 endorsements

    No one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.

    Discussion of this attempt

    no comments

Discussion

no comments

Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.

Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.