Research map / Learning theory and algorithms / Combinatorial and search optimization
Globally optimal geometric optimization
Solves computer vision problems with certifiably optimal and distributed energy minimization methods.
56 accepted papers at ICML, NeurIPS, ICLR, CVPR and AAAI (2016–2026) · an approach in Combinatorial and search optimization, keyword cluster “objective · multi · solutions”
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Where it stands
Not enough benchmark data Fewer than four papers report the same benchmark, so there is no record to follow.
11 papers in 2023–24 and 4 in 2025–26 (at ICML, NeurIPS, ICLR, CVPR and AAAI); its share of the topic shrank, from 3.2% to 1.1%.
How this is decided
A benchmark is tracked when at least four papers of this approach report their own method on the same dataset and metric in at least two different years. Its record is the best number reported up to 2024 compared with the best reported in 2025–26: still improving means at least 1% better, flat means at most 0.2% better with at least two papers from 2025–26 trying. Numbers on a different scale from the rest (a fraction among percentages) and far outliers are left out. Results come from different papers with different setups, so they are signals, not head-to-head comparisons. The share of papers is counted at ICML, NeurIPS, ICLR, CVPR and AAAI.
How it got here
Most cited paper of each year
- 2016 · GOGMA: Globally-Optimal Gaussian Mixture Alignment (CVPR 2016 · 120 citations)
- 2017 · An Efficient Algebraic Solution to the Perspective-Three-Point Problem (CVPR 2017 · 146 citations)
- 2018 · ICE-BA: Incremental, Consistent and Efficient Bundle Adjustment for Visual-Inertial SLAM (CVPR 2018 · 153 citations)
- 2019 · A Robust and Efficient Algorithm for the PnL Problem Using Algebraic Distance to Approximate the Reprojection Distance (AAAI 2019 · 20 citations)
- 2020 · Globally Optimal Contrast Maximisation for Event-Based Motion Estimation (CVPR 2020 · 56 citations)
- 2021 · Quantum Permutation Synchronization (CVPR 2021 · 37 citations)
- 2022 · A Hybrid Quantum-Classical Algorithm for Robust Fitting (CVPR 2022 · 28 citations)
- 2023 · Revisiting Rolling Shutter Bundle Adjustment: Toward Accurate and Fast Solution (CVPR 2023 · 12 citations)
- 2024 · Locally Rainbow Paths (AAAI 2024 · 1 citation)
- 2025 · Densest k-Subgraph Mining via a Provably Tight Relaxation (AAAI 2025 · 0 citations)
- 2026 · Local-Minima-Preserving Polynomial Relaxation of Ising Problems (ICML 2026)
Earliest papers here
- GOGMA: Globally-Optimal Gaussian Mixture Alignment (CVPR 2016 · 120 citations)
- Efficient Intersection of Three Quadrics and Applications in Computer Vision (CVPR 2016 · 64 citations)
- Pairwise Matching Through Max-Weight Bipartite Belief Propagation (CVPR 2016 · 50 citations)
What has been tried
50 papers here report 407 measured changes (a component added, removed or swapped, compared with a baseline): helped 68%, no clear effect 12%, hurt 14%, mixed 6%. Papers mostly publish changes that helped, so "helped" is over-represented.
Ablations in recent papers
| What was changed | Measured on | Result | Effect | Paper |
|---|---|---|---|---|
| Set diagonal loading parameter λ=1 instead of λ=10 or λ=100 | Facebook · subgraph density | Helped | Densest k-Subgraph Mining via a Provably Tight Relaxation (AAAI 2025 · 0 citations) | |
| add parity checks between HWP layers | H2 noise · Energy (Ha) | -0.7599740203 -> -0.7697837117 | Helped | Rethinking Parity Check Enhanced Symmetry-Preserving Ansatz (NeurIPS 2024 · 0 citations) |
What reviewers will expect
Datasets and baselines named in the 5 papers of this approach from 2024–2026 that have a full-text summary. Leaving out the common ones is a frequent review question.
Baselines
- QAOA · 2 of 5 papers
Recent preprints
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Related approaches
Same keyword cluster
- Constrained neural network optimization (111 papers)
- Unsupervised neural combinatorial optimization (113 papers)
- Decision-focused optimization (97 papers)
- Multi-objective optimization (93 papers)
Elsewhere in the topic
- Logic and answer set programming theory (150 papers)
- Heuristic and local search algorithms (147 papers)
- Classical and HTN planning (145 papers)
- Structure and complexity of constraint reasoning (92 papers)
- Predict-then-optimize learning (89 papers)
- SAT and model counting solvers (89 papers)
- Heuristics for integer programming (60 papers)
- Differentiable and symbolic reasoning (56 papers)
Benchmark numbers, ablations and baseline numbers are extracted by AI from each paper's full text and can be wrong; the paper is the authority. Data: results index of 2026-11-02, citation counts from OpenAlex (2026-10-09).