A Primal-Dual Algorithm for Solving Polyhedral Conic Systems with a Finite-Precision Machine
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Bibliographic record
Abstract
We describe a primal-dual interior-point algorithm that determines which one of two alternative systems, Ax = 0, x ≥ 0, and A<sup>T</sup>y ≤ 0, is strictly feasible, provided that this pair of systems is well-posed. Furthermore, when the second system is strictly feasible, the algorithm returns a strict solution y; when the first system is strictly feasible, the algorithm returns a strict forward-approximate solution x. Here A ∈ ℝ<sup>m × n</sup> is given. Our algorithm works with finite-precision arithmetic. The amount of precision required is adjusted as the algorithm progresses and remains bounded by a measure of well-posedness C(A) of the pair of systems of constraints. The algorithm halts in at most O((m+n)<sup>1/2</sup>(log(m+n)+log(C(A))+|logγ|)) interior-point iterations, where γ ∈ (0, 1) is a parameter specifying the desired degree of accuracy of the forward-approximate solution for the first system. If the feasible system is the second one, the term |log γ| in the bound on the number of iterations can be dropped.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it