Semi-infinite linear programming approaches to semidefinite programming problems
Bibliographic record
Abstract
Interior point methods, the traditional methods for the SDP , are fairly limited in the size of problems they can handle. This paper deals with an LP approach to overcome some of these shortcomings. We begin with a semi-infinite linear programming formulation of the SDP and discuss the issue of its discretization in some detail. We further show that a lemma due Pataki on the geometry of the SDP , implies that no more than O( # k) (where k is the number of constraints in the SDP ) linear constraints are required. To generate these constraints we employ the spectral bundle approach due to Helmberg and Rendl. This scheme recasts any SDP with a bounded primal feasible set as an eigenvalue optimization problem. These are convex nonsmooth problems that can be tackled by bundle methods for nondi#erentiable optimization. Finally we present the rationale for using the columns of the bundle P maintained by the spectral bundle approach, as our linear constraints. We present numerical experiments that demonstrate the e#ciency of the LP approach on two combinatorial examples, namely the max cut and min bisection problems. The LP approach potentially allows one to approximately solve large scale semidefinite programs using state of the art linear solvers. # This work was supported in part by NSF grant numbers CCR--9901822 and DMS9872019 + Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York, 12180 (kartis@rpi.edu). # Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York, 12180 (mitchj@rpi.edu). 1 Moreover one can incorporate these linear programs in a branch and cut approach for solving large scale integer programs. Keywords: Semidefinite Programming, Linear Progra...
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.006 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".