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OP-10364Status unassessedMathematics · general

Smales' 9th problem.

Computational mathematics in computer assisted proofs · AIMPL workshop record

Workshop record · status unassessedAs of 2026-09-10 source snapshot; not a current-status certificationSource & evidence ↓
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Problem statement

Does there exist an algorithm for linear programming over the reals done by an algorithm that is independent of the bit-size. (in the framework of the sci-hierarchy).

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Background

Section context

Here we collect a list of problems collected during the workshop to which one could hope to find a concrete answer.

Progress & source assessment

Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.

Status note in the source

Follow-up comment/question: This is Smale's 9th problem: Find a strongly-polynomial time algorithm which for given matrix AA and bb decides if there is xx such that Ax≥b.Ax \ge b. What is the right input set to obtain a polynomial time algorithm?

References
  1. [1]Computational mathematics in computer assisted proofs · Original question link
  2. [2]AIMPL source bibliography link
  3. [3]AIMPL text license · CC BY-SA 3.0 linkAIM Problem Lists (AIMPL), original contributors; CC BY-SA 3.0. Adaptation: structural TeX converted to Markdown, documented source macros expanded, and source bibliography links added. Mathematical wording retained. These adapted source texts remain under CC BY-SA 3.0.

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