Ceres Solver
Ceres Solver 是 Google 發展的開源 C++ 大規模最佳化程式庫，可求解含邊界限制的非線性最小平方問題與一般無約束最佳化。官方版本歷史說明其於 2010 年開始開發、2012 年 5 月開源釋出，並提供軟體引用格式（無 DOI）。本群集中 Cioffi 等人的連續與離散時間比較即以其 Levenberg-Marquardt 與自動微分求解。
本頁內容
Ceres Solver is Google's open-source C++ library for bounded nonlinear least squares and unconstrained optimization, released in May 2012 and cited via a software citation without DOI.
技術屬性
欄位內容為文獻擷取紀錄的原文用語（英文），以原文為據；「未查證」表示本研究尚未讀到該資訊，不代表該方法不具備此能力。
| 感測輸入 | 未記錄 |
|---|---|
| 原文測試平台 | 未記錄 |
| 狀態估計 | robustified, bounds-constrained nonlinear least squares and general unconstrained optimization: trust-region solvers (Levenberg-Marquardt, traditional and subspace Dogleg) and line-search solvers (nonlinear CG, BFGS, LBFGS); linear solvers DENSE_QR, DENSE_NORMAL_CHOLESKY, SPARSE_NORMAL_CHOLESKY, CGNR, DENSE_SCHUR, SPARSE_SCHUR and ITERATIVE_SCHUR, plus a Schur power series expansion (Power Bundle Adjustment) that is enabled through ITERATIVE_SCHUR options rather than as a separate solver type; automatic, numeric and analytic derivatives; loss functions (Huber, SoftLOne, Cauchy, Arctan, Tolerant, Tukey); Manifold parameterizations (e.g. QuaternionManifold); covariance estimation |
| 資料關聯 | 不適用 |
| 時間表示 | 不適用 |
| 去畸變 | 不適用 |
| 迴圈閉合 | 不適用 |
| 全域最佳化 | 不適用 |
| 地圖表示 | 不適用 |
| 先驗資訊 | 不適用 |
| 可輸出幾何 | 不適用 |
| 計算需求 | C++ library; version 2.2.0 requires a C++17 compiler and CMake 3.16 or later, uses C++ threads for multithreading and can use CUDA on NVIDIA GPUs for dense solvers and CGNR; runs on Linux, Windows, macOS, Android and iOS |
使用設備
尚未收錄此方法的設備紀錄；設備資料仍在分批查證，沒有紀錄不代表原文未使用任何設備。
作者報告的優勢與限制
優勢
- Feature-rich, mature library used in production at Google since 2010 (README)
- Automatic, numeric and analytic derivatives can be mixed in any combination (features.html)
- Schur-complement-based dense, sparse and iterative linear solvers for bundle adjustment, and covariance estimation at scale (features.html)
- Self-reported as the best performing solver on the NIST problem set used by Mondragon and Borchers (features.html; not independently verified here)
限制
- No DOI-based archival record found; citation relies on CITATION.cff or website bibtex (inference from sources checked)
- Finds a local minimum; the documentation states efficient global minimization is intractable in general (nnls_solving.html, Introduction)
- Version 2.2.0 removed LocalParameterization (replaced by Manifold) and dropped the OpenMP, NO_THREADING and CX_SPARSE backends, so older integrations may need changes (version_history.html)
- The documentation gives inconsistent start years for production use at Google (2010 on index and README, 2011 on features.html)
營建工程相關證據
未在營建場域驗證；官方使用者清單提到 Matterport 以 Ceres 進行三維點雲全域對齊與位姿圖最佳化（users.html），此類室內掃描用途與營建紀錄的關聯屬推論。
報告的性能數據
性能數據仍在分批查證，目前尚未收錄此方法的報告值。
來源
Agarwal et al., 2023
（2023）Ceres SolverSoftware (GitHub ceres-solver/ceres-solver; ceres-solver.org), version 2.2 (CITATION.cff date-released 2023-10-13)
軟體或資料集紀錄已讀部分章節經典查證後修正
程式碼：https://github.com/ceres-solver/ceres-solver（授權：Official license page: New BSD (3-clause) for Ceres itself; the repository LICENSE file reproduces the BSD text followed by the full Apache-2.0 text and an MIT notice for libmv-derived example code; CITATION.cff and website bibtex list Apache-2.0. State 'BSD (per ceres-solver.org/license.html)' and note the Apache-2.0 metadata discrepancy）。有公開程式碼不等於已被重現，也不代表目前版本與論文版本相同。