Interior Point Solution of Multilevel Quadratic Programming Problems in Constrained Model Predictive Control Applications
Bibliographic record
Abstract
This paper examines the use of an interior point strategy to solve multilevel optimization problems that arise from the inclusion of the closed-loop response of constrained, linear model predictive control (MPC) within a primary quadratic or linear programming problem. We motivate the formulation through its application to optimizing control problems, although the strategy is applicable to several problem types. The problem is cast as a dynamic optimization problem in which an optimal steady-state operating point is sought, subject to constraints on the closed-loop response of the system under constrained predictive control. Because a quadratic programming (QP) problem must be solved at every sampling period, the resulting problem is multilevel in nature. The formulation approach used in this paper is to include the Karush−Kuhn−Tucker (KKT) conditions that correspond to the MPC quadratic programming subproblems as constraints within a single-level optimization problem. The resulting complementarity constrained optimization problem is shown to be reliably and efficiently solved using an interior point approach. The method is applied to two case studies, and its performance is compared to an alternative mixed-integer programming solution approach.
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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 | 0.002 | 0.003 |
| 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) | 0.002 | 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 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".