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Refine other optimizers' docs

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61
gtsam/nonlinear/doc/GaussNewtonOptimizer.ipynb
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"id": "6463d580", "id": "6463d580",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# GaussNewtonOptimizer Class Documentation\n", "# GaussNewtonOptimizer\n",
"\n",
"*Disclaimer: This documentation was generated by AI and may require human revision for accuracy and completeness.*\n",
"\n", "\n",
"## Overview\n", "## Overview\n",
"\n", "\n",
"The `GaussNewtonOptimizer` class in GTSAM is designed to optimize nonlinear factor graphs using the Gauss-Newton algorithm. This class is particularly suited for problems where the cost function can be approximated well by a quadratic function near the minimum. The Gauss-Newton method is an iterative optimization technique that updates the solution by linearizing the nonlinear system at each iteration.\n", "The `GaussNewtonOptimizer` class in GTSAM is designed to optimize nonlinear factor graphs using the Gauss-Newton algorithm. This class is particularly suited for problems where the cost function can be approximated well by a quadratic function near the minimum. The Gauss-Newton method is an iterative optimization technique that updates the solution by linearizing the nonlinear system at each iteration.\n",
"\n", "\n",
"## Key Features\n",
"\n",
"- **Iterative Optimization**: The optimizer refines the solution iteratively by linearizing the nonlinear system around the current estimate.\n",
"- **Convergence Control**: It provides mechanisms to control the convergence through parameters such as maximum iterations and relative error tolerance.\n",
"- **Integration with GTSAM**: Seamlessly integrates with GTSAM's factor graph framework, allowing it to be used with various types of factors and variables.\n",
"\n",
"## Key Methods\n",
"\n",
"### Constructor\n",
"\n",
"- **GaussNewtonOptimizer**: Initializes the optimizer with a given factor graph and initial values. The constructor sets up the optimization problem and prepares it for iteration.\n",
"\n",
"### Optimization\n",
"\n",
"- **optimize**: Executes the optimization process. This method runs the Gauss-Newton iterations until convergence criteria are met, such as reaching the maximum number of iterations or achieving a relative error below a specified threshold.\n",
"\n",
"### Convergence Criteria\n",
"\n",
"- **checkConvergence**: Evaluates whether the optimization process has converged based on the change in error and the specified tolerance levels.\n",
"\n",
"### Accessors\n",
"\n",
"- **error**: Returns the current error of the factor graph with respect to the current estimate. This is useful for monitoring the progress of the optimization.\n",
"- **values**: Retrieves the current estimate of the variable values after optimization.\n",
"\n",
"## Mathematical Background\n",
"\n",
"The Gauss-Newton algorithm is based on the idea of linearizing the nonlinear residuals $r(x)$ around the current estimate $x_k$. The update step is derived from solving the normal equations:\n", "The Gauss-Newton algorithm is based on the idea of linearizing the nonlinear residuals $r(x)$ around the current estimate $x_k$. The update step is derived from solving the normal equations:\n",
"\n", "\n",
"$$ J(x_k)^T J(x_k) \\Delta x = -J(x_k)^T r(x_k) $$\n", "$$ J(x_k)^T J(x_k) \\Delta x = -J(x_k)^T r(x_k) $$\n",
@ -50,17 +21,43 @@
"\n", "\n",
"This process is repeated iteratively until convergence.\n", "This process is repeated iteratively until convergence.\n",
"\n", "\n",
"Key features:\n",
"\n",
"- **Iterative Optimization**: The optimizer refines the solution iteratively by linearizing the nonlinear system around the current estimate.\n",
"- **Convergence Control**: It provides mechanisms to control the convergence through parameters such as maximum iterations and relative error tolerance.\n",
"- **Integration with GTSAM**: Seamlessly integrates with GTSAM's factor graph framework, allowing it to be used with various types of factors and variables.\n",
"\n",
"## Key Methods\n",
"\n",
"Please see the base class [NonlinearOptimizer.ipynb](NonlinearOptimizer.ipynb).\n",
"\n",
"## Parameters\n",
"\n",
"The Gauss-Newton optimizer uses the standard optimization parameters inherited from `NonlinearOptimizerParams`, which include:\n",
"\n",
"- Maximum iterations\n",
"- Relative and absolute error thresholds\n",
"- Error function verbosity\n",
"- Linear solver type\n",
"\n",
"## Usage Considerations\n", "## Usage Considerations\n",
"\n", "\n",
"- **Initial Guess**: The quality of the initial guess can significantly affect the convergence and performance of the Gauss-Newton optimizer.\n", "- **Initial Guess**: The quality of the initial guess can significantly affect the convergence and performance of the Gauss-Newton optimizer.\n",
"- **Non-convexity**: Since the method relies on linear approximations, it may struggle with highly non-convex problems or those with poor initial estimates.\n", "- **Non-convexity**: Since the method relies on linear approximations, it may struggle with highly non-convex problems or those with poor initial estimates.\n",
"- **Performance**: The Gauss-Newton method is generally faster than other nonlinear optimization methods like Levenberg-Marquardt for problems that are well-approximated by a quadratic model near the solution.\n", "- **Performance**: The Gauss-Newton method is generally faster than other nonlinear optimization methods like Levenberg-Marquardt for problems that are well-approximated by a quadratic model near the solution.\n",
"\n", "\n",
"In summary, the `GaussNewtonOptimizer` is a powerful tool for solving nonlinear optimization problems in factor graphs, particularly when the problem is well-suited to quadratic approximation. Its integration with GTSAM makes it a versatile choice for various applications in robotics and computer vision." "## Files\n",
"\n",
"- [GaussNewtonOptimizer.h](https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/GaussNewtonOptimizer.h)\n",
"- [GaussNewtonOptimizer.cpp](https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/GaussNewtonOptimizer.cpp)"
] ]
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75
gtsam/nonlinear/doc/GncOptimizer.ipynb
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@ -5,42 +5,12 @@
"id": "c950beef", "id": "c950beef",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# GTSAM GncOptimizer Class Documentation\n", "# GncOptimizer\n",
"\n",
"*Disclaimer: This documentation was generated by AI and requires human revision to ensure accuracy and completeness.*\n",
"\n", "\n",
"## Overview\n", "## Overview\n",
"\n", "\n",
"The `GncOptimizer` class in GTSAM is designed to perform robust optimization using Graduated Non-Convexity (GNC). This method is particularly useful in scenarios where the optimization problem is affected by outliers. The GNC approach gradually transitions from a convex approximation of the problem to the original non-convex problem, thereby improving robustness and convergence.\n", "The `GncOptimizer` class in GTSAM is designed to perform robust optimization using Graduated Non-Convexity (GNC). This method is particularly useful in scenarios where the optimization problem is affected by outliers. The GNC approach gradually transitions from a convex approximation of the problem to the original non-convex problem, thereby improving robustness and convergence.\n",
"\n", "\n",
"## Key Features\n",
"\n",
"- **Robust Optimization**: The `GncOptimizer` is specifically tailored to handle optimization problems with outliers, using a robust cost function that can mitigate their effects.\n",
"- **Graduated Non-Convexity**: This technique allows the optimizer to start with a convex problem and gradually transform it into the original non-convex problem, which helps in avoiding local minima.\n",
"- **Customizable Parameters**: Users can adjust various parameters to control the behavior of the optimizer, such as the type of robust loss function and the parameters governing the GNC process.\n",
"\n",
"## Key Methods\n",
"\n",
"### Initialization and Setup\n",
"\n",
"- **Constructor**: The class constructor initializes the optimizer with a given nonlinear factor graph and initial estimate. It also accepts parameters specific to the GNC process.\n",
"\n",
"### Optimization Process\n",
"\n",
"- **optimize()**: This method performs the optimization process. It iteratively refines the solution by adjusting the influence of the robust cost function, following the principles of graduated non-convexity.\n",
"\n",
"### Configuration and Parameters\n",
"\n",
"- **setParams()**: Allows users to set the parameters for the GNC optimization process, including the type of robust loss function and other algorithm-specific settings.\n",
"- **getParams()**: Retrieves the current parameters used by the optimizer, providing insight into the configuration of the optimization process.\n",
"\n",
"### Utility Functions\n",
"\n",
"- **cost()**: Computes the cost of the current estimate, which is useful for evaluating the progress of the optimization.\n",
"- **error()**: Returns the error associated with the current estimate, offering a measure of how well the optimization is performing.\n",
"\n",
"## Mathematical Formulation\n",
"\n",
"The `GncOptimizer` leverages a robust cost function $\\rho(e)$, where $e$ is the error term. The goal is to minimize the sum of these robust costs over all measurements:\n", "The `GncOptimizer` leverages a robust cost function $\\rho(e)$, where $e$ is the error term. The goal is to minimize the sum of these robust costs over all measurements:\n",
"\n", "\n",
"$$\n", "$$\n",
@ -55,16 +25,55 @@
"\n", "\n",
"As $\\mu$ increases, the function $\\rho_\\mu(e)$ transitions from a convex to a non-convex shape, allowing the optimizer to handle outliers effectively.\n", "As $\\mu$ increases, the function $\\rho_\\mu(e)$ transitions from a convex to a non-convex shape, allowing the optimizer to handle outliers effectively.\n",
"\n", "\n",
"Key features:\n",
"\n",
"- **Robust Optimization**: The GncOptimizer is specifically tailored to handle optimization problems with outliers, using a robust cost function that can mitigate their effects.\n",
"- **Graduated Non-Convexity**: This technique allows the optimizer to start with a convex problem and gradually transform it into the original non-convex problem, which helps in avoiding local minima.\n",
"- **Customizable Parameters**: Users can adjust various parameters to control the behavior of the optimizer, such as the type of robust loss function and the parameters governing the GNC process.\n",
"\n",
"## Key Methods\n",
"\n",
"Please see the base class [NonlinearOptimizer.ipynb](NonlinearOptimizer.ipynb).\n",
"\n",
"## Parameters\n",
"\n",
"The `GncParams` class defines parameters specific to the GNC optimization algorithm:\n",
"\n",
"| Parameter | Type | Default Value | Description |\n",
"|-----------|------|---------------|-------------|\n",
"| lossType | GncLossType | TLS | Type of robust loss function (GM = Geman McClure or TLS = Truncated least squares) |\n",
"| maxIterations | size_t | 100 | Maximum number of iterations |\n",
"| muStep | double | 1.4 | Multiplicative factor to reduce/increase mu in GNC |\n",
"| relativeCostTol | double | 1e-5 | Threshold for relative cost change to stop iterating |\n",
"| weightsTol | double | 1e-4 | Threshold for weights being close to binary to stop iterating (TLS only) |\n",
"| verbosity | Verbosity enum | SILENT | Verbosity level (options: SILENT, SUMMARY, MU, WEIGHTS, VALUES) |\n",
"| knownInliers | IndexVector | Empty | Slots in factor graph for measurements known to be inliers |\n",
"| knownOutliers | IndexVector | Empty | Slots in factor graph for measurements known to be outliers |\n",
"\n",
"These parameters complement the standard optimization parameters inherited from `NonlinearOptimizerParams`, which include:\n",
"\n",
"- Maximum iterations\n",
"- Relative and absolute error thresholds\n",
"- Error function verbosity\n",
"- Linear solver type\n",
"\n",
"## Usage Considerations\n", "## Usage Considerations\n",
"\n", "\n",
"- **Outlier Rejection**: The `GncOptimizer` is particularly effective in scenarios with significant outlier presence, such as SLAM or bundle adjustment problems.\n", "- **Outlier Rejection**: The `GncOptimizer` is particularly effective in scenarios with significant outlier presence, such as SLAM or bundle adjustment problems.\n",
"- **Parameter Tuning**: Proper tuning of the GNC parameters is crucial for achieving optimal performance. Users should experiment with different settings to find the best configuration for their specific problem.\n", "- **Parameter Tuning**: Proper tuning of the GNC parameters is crucial for achieving optimal performance. Users should experiment with different settings to find the best configuration for their specific problem.\n",
"\n", "\n",
"This high-level overview provides a starting point for understanding and utilizing the `GncOptimizer` class in GTSAM. For detailed implementation and advanced usage, users should refer to the source code and additional GTSAM documentation." "## Files\n",
"\n",
"- [GncOptimizer.h](https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/GncOptimizer.h)\n",
"- [GncParams.h](https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/GncParams.h)"
] ]
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gtsam/nonlinear/doc/LevenbergMarquardtOptimizer.ipynb
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@ -5,9 +5,7 @@
"id": "29642bb2", "id": "29642bb2",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# LevenbergMarquardtOptimizer Class Documentation\n", "# LevenbergMarquardtOptimizer\n",
"\n",
"*Disclaimer: This documentation was generated by AI and may require human revision for accuracy and completeness.*\n",
"\n", "\n",
"## Overview\n", "## Overview\n",
"\n", "\n",
@ -15,14 +13,6 @@
"\n", "\n",
"The Levenberg-Marquardt algorithm is an iterative technique that interpolates between the Gauss-Newton algorithm and the method of gradient descent. It is particularly useful for optimizing problems where the solution is expected to be near the initial guess.\n", "The Levenberg-Marquardt algorithm is an iterative technique that interpolates between the Gauss-Newton algorithm and the method of gradient descent. It is particularly useful for optimizing problems where the solution is expected to be near the initial guess.\n",
"\n", "\n",
"## Key Features\n",
"\n",
"- **Non-linear Optimization**: The class is designed to handle non-linear optimization problems efficiently.\n",
"- **Damping Mechanism**: It incorporates a damping parameter to control the step size, balancing between the Gauss-Newton and gradient descent methods.\n",
"- **Iterative Improvement**: The optimizer iteratively refines the solution, reducing the error at each step.\n",
"\n",
"## Mathematical Formulation\n",
"\n",
"The Levenberg-Marquardt algorithm seeks to minimize a cost function $F(x)$ of the form:\n", "The Levenberg-Marquardt algorithm seeks to minimize a cost function $F(x)$ of the form:\n",
"\n", "\n",
"$$\n", "$$\n",
@ -37,25 +27,40 @@
"\n", "\n",
"Here, $J$ is the Jacobian matrix of the residuals, $\\lambda$ is the damping parameter, and $I$ is the identity matrix.\n", "Here, $J$ is the Jacobian matrix of the residuals, $\\lambda$ is the damping parameter, and $I$ is the identity matrix.\n",
"\n", "\n",
"Key features:\n",
"\n",
"- **Non-linear Optimization**: The class is designed to handle non-linear optimization problems efficiently.\n",
"- **Damping Mechanism**: It incorporates a damping parameter to control the step size, balancing between the Gauss-Newton and gradient descent methods.\n",
"- **Iterative Improvement**: The optimizer iteratively refines the solution, reducing the error at each step.\n",
"\n",
"## Key Methods\n", "## Key Methods\n",
"\n", "\n",
"### Initialization\n", "Please see the base class [NonlinearOptimizer.ipynb](NonlinearOptimizer.ipynb).\n",
"\n", "\n",
"- **Constructor**: Initializes the optimizer with the given parameters and initial values.\n", "## Parameters\n",
"\n", "\n",
"### Optimization\n", "The `LevenbergMarquardtParams` class defines parameters specific to this optimization algorithm:\n",
"\n", "\n",
"- **optimize**: Executes the optimization process, iteratively updating the solution to minimize the cost function.\n", "| Parameter | Type | Default Value | Description |\n",
"|-----------|------|---------------|-------------|\n",
"| lambdaInitial | double | 1e-5 | The initial Levenberg-Marquardt damping term |\n",
"| lambdaFactor | double | 10.0 | The amount by which to multiply or divide lambda when adjusting lambda |\n",
"| lambdaUpperBound | double | 1e5 | The maximum lambda to try before assuming the optimization has failed |\n",
"| lambdaLowerBound | double | 0.0 | The minimum lambda used in LM |\n",
"| verbosityLM | VerbosityLM | SILENT | The verbosity level for Levenberg-Marquardt |\n",
"| minModelFidelity | double | 1e-3 | Lower bound for the modelFidelity to accept the result of an LM iteration |\n",
"| logFile | std::string | \"\" | An optional CSV log file, with [iteration, time, error, lambda] |\n",
"| diagonalDamping | bool | false | If true, use diagonal of Hessian |\n",
"| useFixedLambdaFactor | bool | true | If true applies constant increase (or decrease) to lambda according to lambdaFactor |\n",
"| minDiagonal | double | 1e-6 | When using diagonal damping saturates the minimum diagonal entries |\n",
"| maxDiagonal | double | 1e32 | When using diagonal damping saturates the maximum diagonal entries |\n",
"\n", "\n",
"### Parameter Control\n", "These parameters complement the standard optimization parameters inherited from `NonlinearOptimizerParams`, which include:\n",
"\n", "\n",
"- **setLambda**: Sets the damping parameter $\\lambda$, which influences the convergence behavior.\n", "- Maximum iterations\n",
"- **getLambda**: Retrieves the current value of the damping parameter.\n", "- Relative and absolute error thresholds\n",
"\n", "- Error function verbosity\n",
"### Convergence and Termination\n", "- Linear solver type\n",
"\n",
"- **checkConvergence**: Evaluates whether the optimization process has converged based on predefined criteria.\n",
"- **terminate**: Stops the optimization process when certain conditions are met.\n",
"\n", "\n",
"## Usage Notes\n", "## Usage Notes\n",
"\n", "\n",
@ -63,11 +68,20 @@
"- Proper tuning of the damping parameter $\\lambda$ is crucial for balancing the convergence rate and stability.\n", "- Proper tuning of the damping parameter $\\lambda$ is crucial for balancing the convergence rate and stability.\n",
"- The optimizer is most effective when the residuals are approximately linear near the solution.\n", "- The optimizer is most effective when the residuals are approximately linear near the solution.\n",
"\n", "\n",
"This class is a powerful tool for tackling complex optimization problems where traditional linear methods fall short. By leveraging the strengths of both Gauss-Newton and gradient descent, the `LevenbergMarquardtOptimizer` provides a robust framework for achieving accurate solutions in non-linear least squares problems." "## Files\n",
"\n",
"- [LevenbergMarquardtOptimizer.h](https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/LevenbergMarquardtOptimizer.h)\n",
"- [LevenbergMarquardtOptimizer.cpp](https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/LevenbergMarquardtOptimizer.cpp)\n",
"- [LevenbergMarquardtParams.h](https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/LevenbergMarquardtParams.h)\n",
"- [LevenbergMarquardtParams.cpp](https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/LevenbergMarquardtParams.cpp)"
] ]
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gtsam/nonlinear/doc/NonlinearConjugateGradientOptimizer.ipynb
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@ -5,37 +5,12 @@
"id": "48970ca0", "id": "48970ca0",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# NonlinearConjugateGradientOptimizer Class Documentation\n", "# NonlinearConjugateGradientOptimizer\n",
"\n",
"*Disclaimer: This documentation was generated by AI and may require human revision for accuracy and completeness.*\n",
"\n", "\n",
"## Overview\n", "## Overview\n",
"\n", "\n",
"The `NonlinearConjugateGradientOptimizer` class in GTSAM is an implementation of the nonlinear conjugate gradient method for optimizing nonlinear functions. This optimizer is particularly useful for solving large-scale optimization problems where the Hessian matrix is not easily computed or stored. The conjugate gradient method is an iterative algorithm that seeks to find the minimum of a function by following a series of conjugate directions.\n", "The `NonlinearConjugateGradientOptimizer` class in GTSAM is an implementation of the nonlinear conjugate gradient method for optimizing nonlinear functions. This optimizer is particularly useful for solving large-scale optimization problems where the Hessian matrix is not easily computed or stored. The conjugate gradient method is an iterative algorithm that seeks to find the minimum of a function by following a series of conjugate directions.\n",
"\n", "\n",
"## Key Features\n",
"\n",
"- **Optimization Method**: Implements the nonlinear conjugate gradient method, which is an extension of the linear conjugate gradient method to nonlinear optimization problems.\n",
"- **Efficiency**: Suitable for large-scale problems due to its iterative nature and reduced memory requirements compared to methods that require the Hessian matrix.\n",
"- **Flexibility**: Can be used with various line search strategies and conjugate gradient update formulas.\n",
"\n",
"## Main Methods\n",
"\n",
"### Constructor\n",
"\n",
"- **NonlinearConjugateGradientOptimizer**: Initializes the optimizer with a given nonlinear factor graph and initial values. The user can specify optimization parameters, including the choice of line search method and conjugate gradient update formula.\n",
"\n",
"### Optimization\n",
"\n",
"- **optimize**: Executes the optimization process. This method iteratively updates the solution by computing search directions and performing line searches to minimize the objective function along these directions.\n",
"\n",
"### Accessors\n",
"\n",
"- **error**: Returns the current error value of the objective function. This is useful for monitoring the convergence of the optimization process.\n",
"- **values**: Retrieves the current estimate of the optimized variables. This allows users to access the solution at any point during the optimization.\n",
"\n",
"## Mathematical Background\n",
"\n",
"The nonlinear conjugate gradient method seeks to minimize a nonlinear function $f(x)$ by iteratively updating the solution $x_k$ according to:\n", "The nonlinear conjugate gradient method seeks to minimize a nonlinear function $f(x)$ by iteratively updating the solution $x_k$ according to:\n",
"\n", "\n",
"$$ x_{k+1} = x_k + \\alpha_k p_k $$\n", "$$ x_{k+1} = x_k + \\alpha_k p_k $$\n",
@ -50,17 +25,43 @@
"\n", "\n",
"The choice of $\\beta_k$ affects the convergence properties of the algorithm.\n", "The choice of $\\beta_k$ affects the convergence properties of the algorithm.\n",
"\n", "\n",
"Key features:\n",
"\n",
"- **Optimization Method**: Implements the nonlinear conjugate gradient method, which is an extension of the linear conjugate gradient method to nonlinear optimization problems.\n",
"- **Efficiency**: Suitable for large-scale problems due to its iterative nature and reduced memory requirements compared to methods that require the Hessian matrix.\n",
"- **Flexibility**: Can be used with various line search strategies and conjugate gradient update formulas.\n",
"\n",
"## Key Methods\n",
"\n",
"Please see the base class [NonlinearOptimizer.ipynb](NonlinearOptimizer.ipynb).\n",
"\n",
"## Parameters\n",
"\n",
"The nonlinear conjugate gradient optimizer uses the standard optimization parameters inherited from `NonlinearOptimizerParams`, which include:\n",
"\n",
"- Maximum iterations\n",
"- Relative and absolute error thresholds\n",
"- Error function verbosity\n",
"- Linear solver type\n",
"\n",
"## Usage Notes\n", "## Usage Notes\n",
"\n", "\n",
"- The `NonlinearConjugateGradientOptimizer` is most effective when the problem size is large and the computation of the Hessian is impractical.\n", "- The `NonlinearConjugateGradientOptimizer` is most effective when the problem size is large and the computation of the Hessian is impractical.\n",
"- Users should choose an appropriate line search method and conjugate gradient update formula based on the specific characteristics of their optimization problem.\n", "- Users should choose an appropriate line search method and conjugate gradient update formula based on the specific characteristics of their optimization problem.\n",
"- Monitoring the error and values during optimization can provide insights into the convergence behavior and help diagnose potential issues.\n", "- Monitoring the error and values during optimization can provide insights into the convergence behavior and help diagnose potential issues.\n",
"\n", "\n",
"This class provides a robust framework for solving complex nonlinear optimization problems efficiently, leveraging the power of the conjugate gradient method." "## Files\n",
"\n",
"- [NonlinearConjugateGradientOptimizer.h](https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/NonlinearConjugateGradientOptimizer.h)\n",
"- [NonlinearConjugateGradientOptimizer.cpp](https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/NonlinearConjugateGradientOptimizer.cpp)"
] ]
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