Piecewise Linear Plus Quadratic Surrogate Model for Real-Time Optimization
Bibliographic record
Abstract
Surrogate models are important in real-time optimization (RTO) when the first-principles model is unavailable or computationally challenging for online optimization. Among different surrogate models, the continuous piecewise linear (CPWL) model enjoys the universal approximation ability and potential computational benefits. However, the CPWL surrogate model poses three challenges to current RTO algorithms. First, the solution of a CPWL model is always located on the boundary of a polytopic subregion, while the plant optimum may be in the interior of a subregion. Second, the CPWL model is nonsmooth, which cannot be handled by RTO methods that rely on gradient matching. Third, the resulting nonsmooth optimization subproblems are hard to solve. This paper addresses the difficulties by adding a quadratic function to the CPWL surrogate model, extending a classical RTO method to accommodate nonsmoothness, and exploiting the diffierence-of-convex structure of the surrogate model for Efficient solution. The advantages of the proposed method are demonstrated through a benchmark problem in the RTO literature.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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".