Convergence of a new nonmonotone memory gradient method for unconstrained multiobjective optimization via robust approach
Bibliographic record
Abstract
Robust approach is a special scalarization method to deal with multiobjective optimization problems in the worst-case.In this paper, we propose a new non-monotone gradient type algorithm for solving unconstrained multiobjective optimization problems by the conjugate technique and the robust approach.The proposed method has a memory gradient property since the search direction is constructed by using the current descent direction and the past multi-step iterative descent directions.For this, the search direction is called a memory gradient search direction.The step-size is computed by the nonmonotone linear search.A lower bound of the stepsize is presented under some mild conditions.Then the iterative sequence generated by the proposed method is proved to be convergent to a Pareto critical point of the multiobjective optimization problem under some mild conditions.Numerical experiments are reported to show the effectiveness of the proposed method.
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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 | 0.001 |
| 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".