Generalized quadratically constrained quadratic programming for signal processing
Bibliographic record
Abstract
In this paper, we introduce and solve a particular generalization of the quadratically constrained quadratic programming (QCQP) problem which is frequently encountered in different fields of signal processing and communications. Specifically, we consider such generalization of the QCQP problem that comprises compositions of one-dimensional convex and quadratic functions in the constraint and the objective functions. We show that this class of problems can be precisely or approximately recast as the difference-of-convex functions (DC) programming problem. Although the DC programming problem can be solved through the branch-and-bound methods, these methods do not have any worst-case polynomial-time complexity guarantees. Therefore, we develop a new approach with worst-case polynomial-time complexity that can solve the corresponding DC problem of a generalized QCQP problem. It is analytically guaranteed that the point obtained by this method satisfies the Karsuh-Kuhn-Tucker (KKT) optimality conditions. Furthermore, the global optimality can be proved analytically under certain conditions. The new proposed method can be interpreted in terms of the Newton's method as applied to a non-constrained optimization problem.
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How this classification was reachedexpand
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 | 0.000 | 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 |
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 teacher head, 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".