A Scaled Gauss--Newton Primal-Dual Search Direction for Semidefinite Optimization
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Bibliographic record
Abstract
Interior point methods for semidefinite optimization (SDO) have recently been studied intensively, due to their polynomial complexity and practical efficiency. Most of these methods are extensions of linear optimization (LO) algorithms. As opposed to the LO case, there are several different ways of constructing primal-dual search directions in SDO. The usual scheme is to apply linearization in conjunction with symmetrization to the perturbed optimality conditions of the SDO problem. Symmetrization is necessary since the linearized system is overdetermined. A way of avoiding symmetrization is to find a least squares solution of the overdetermined system. Such a "Gauss--Newton" direction was investigated by Kruk et al. [The Gauss--Newton Direction in Semidefinite Programming, Research report CORR 98-16, University of Waterloo, Waterloo, Canada, 1998] without giving any complexity analysis. In this paper we present a similar direction where a local norm is used in the least squares formulation, and we give a polynomial complexity analysis and computational evaluation of the resulting primal-dual algorithm.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
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