--- name: "mlpack_optimization_L_BFGS" section: "3" platform: "linux" package: "mlpack-doc" version: "1.0.10-1" release: "Debian 8 (Jessie)" platforms: ["linux"] url: "https://new.carta.tech/mlpack_optimization_L_BFGS" --- # mlpack\_optimization\_L\_BFGS(3) The generic L-BFGS optimizer, which uses a back-tracking line search algorithm to minimize a function. ## NAME mlpack::optimization::L\_BFGS\< FunctionType \> - The generic L-BFGS optimizer, which uses a back-tracking line search algorithm to minimize a function. ## SYNOPSIS ### Public Member Functions **L\_BFGS** (FunctionType &**function**, const size\_t **numBasis**=5, const size\_t **maxIterations**=0, const double **armijoConstant**=1e-4, const double wolfe=0.9, const double minGradientNorm=1e-10, const size\_t maxLineSearchTrials=50, const double minStep=1e-20, const double maxStep=1e20)\ *Initialize the L-BFGS object.* double **ArmijoConstant** () const \ *Get the Armijo condition constant.* double & **ArmijoConstant** ()\ *Modify the Armijo condition constant.* const FunctionType & **Function** () const \ *Return the function that is being optimized.* FunctionType & **Function** ()\ *Modify the function that is being optimized.* size\_t **MaxIterations** () const \ *Get the maximum number of iterations.* size\_t & **MaxIterations** ()\ *Modify the maximum number of iterations.* size\_t **MaxLineSearchTrials** () const \ *Get the maximum number of line search trials.* size\_t & **MaxLineSearchTrials** ()\ *Modify the maximum number of line search trials.* double **MaxStep** () const \ *Return the maximum line search step size.* double & **MaxStep** ()\ *Modify the maximum line search step size.* double **MinGradientNorm** () const \ *Get the minimum gradient norm.* double & **MinGradientNorm** ()\ *Modify the minimum gradient norm.* const std::pair\< arma::mat, \ double \> & **MinPointIterate** () const "\ *Return the point where the lowest function value has been found.* double **MinStep** () const \ *Return the minimum line search step size.* double & **MinStep** ()\ *Modify the minimum line search step size.* size\_t **NumBasis** () const \ *Get the memory size.* size\_t & **NumBasis** ()\ *Modify the memory size.* double **Optimize** (arma::mat &iterate)\ *Use L-BFGS to optimize the given function, starting at the given iterate point and finding the minimum.* double **Optimize** (arma::mat &iterate, const size\_t **maxIterations**)\ *Use L-BFGS to optimize (minimize) the given function, starting at the given iterate point, and performing no more than the given maximum number of iterations (the class variable maxIterations is ignored for this run, but not modified).* std::string **ToString** () const \ double **Wolfe** () const \ *Get the Wolfe parameter.* double & **Wolfe** ()\ *Modify the Wolfe parameter.* ### Private Member Functions double **ChooseScalingFactor** (const size\_t iterationNum, const arma::mat &gradient)\ *Calculate the scaling factor, gamma, which is used to scale the Hessian approximation matrix.* double **Evaluate** (const arma::mat &iterate)\ *Evaluate the function at the given iterate point and store the result if it is a new minimum.* bool **GradientNormTooSmall** (const arma::mat &gradient)\ *Check to make sure that the norm of the gradient is not smaller than 1e-5.* bool **LineSearch** (double &functionValue, arma::mat &iterate, arma::mat &gradient, const arma::mat &searchDirection)\ *Perform a back-tracking line search along the search direction to calculate a step size satisfying the Wolfe conditions.* void **SearchDirection** (const arma::mat &gradient, const size\_t iterationNum, const double scalingFactor, arma::mat &searchDirection)\ *Find the L-BFGS search direction.* void **UpdateBasisSet** (const size\_t iterationNum, const arma::mat &iterate, const arma::mat &oldIterate, const arma::mat &gradient, const arma::mat &oldGradient)\ *Update the y and s matrices, which store the differences between the iterate and old iterate and the differences between the gradient and the old gradient, respectively.* ### Private Attributes double **armijoConstant**\ *Parameter for determining the Armijo condition.* FunctionType & **function**\ *Internal reference to the function we are optimizing.* size\_t **maxIterations**\ *Maximum number of iterations.* size\_t **maxLineSearchTrials**\ *Maximum number of trials for the line search.* double **maxStep**\ *Maximum step of the line search.* double **minGradientNorm**\ *Minimum gradient norm required to continue the optimization.* std::pair\< arma::mat, double \> **minPointIterate**\ *Best point found so far.* double **minStep**\ *Minimum step of the line search.* arma::mat **newIterateTmp**\ *Position of the new iterate.* size\_t **numBasis**\ *Size of memory for this L-BFGS optimizer.* arma::cube **s**\ *Stores all the s matrices in memory.* double **wolfe**\ *Parameter for detecting the Wolfe condition.* arma::cube **y**\ *Stores all the y matrices in memory.* ## Detailed Description ### template\class mlpack::optimization::L\_BFGS\< FunctionType \> The generic L-BFGS optimizer, which uses a back-tracking line search algorithm to minimize a function. The parameters for the algorithm (number of memory points, maximum step size, and so forth) are all configurable via either the constructor or standalone modifier functions. A function which can be optimized by this class must implement the following methods: - • a default constructor - • double **Evaluate(const arma::mat& coordinates)**; - • void Gradient(const arma::mat& coordinates, arma::mat& gradient); - • arma::mat& GetInitialPoint(); Definition at line 44 of file lbfgs.hpp. ## Constructor & Destructor Documentation ### template\ mlpack::optimization::L\_BFGS\< FunctionType \>::L\_BFGS (FunctionType &function, const size\_tnumBasis = `5`, const size\_tmaxIterations = `0`, const doublearmijoConstant = `1e-4`, const doublewolfe = `0.9`, const doubleminGradientNorm = `1e-10`, const size\_tmaxLineSearchTrials = `50`, const doubleminStep = `1e-20`, const doublemaxStep = `1e20`) Initialize the L-BFGS object. Store a reference to the function we will be optimizing and set the size of the memory for the algorithm. There are many parameters that can be set for the optimization, but default values are given for each of them. **Parameters:** *function* Instance of function to be optimized. \ *numBasis* Number of memory points to be stored (default 5). \ *maxIterations* Maximum number of iterations for the optimization (default 0 -- may run indefinitely). \ *armijoConstant* Controls the accuracy of the line search routine for determining the Armijo condition. \ *wolfe* Parameter for detecting the Wolfe condition. \ *minGradientNorm* Minimum gradient norm required to continue the optimization. \ *maxLineSearchTrials* The maximum number of trials for the line search (before giving up). \ *minStep* The minimum step of the line search. \ *maxStep* The maximum step of the line search. ## Member Function Documentation ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::ArmijoConstant () const` [inline]` Get the Armijo condition constant. Definition at line 128 of file lbfgs.hpp. ### template\ double& mlpack::optimization::L\_BFGS\< FunctionType \>::ArmijoConstant ()` [inline]` Modify the Armijo condition constant. Definition at line 130 of file lbfgs.hpp. ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::ChooseScalingFactor (const size\_titerationNum, const arma::mat &gradient)` [private]` Calculate the scaling factor, gamma, which is used to scale the Hessian approximation matrix. See method M3 in Section 4 of Liu and Nocedal (1989). **Returns:** The calculated scaling factor. ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::Evaluate (const arma::mat &iterate)` [private]` Evaluate the function at the given iterate point and store the result if it is a new minimum. **Returns:** The value of the function. ### template\ const FunctionType& mlpack::optimization::L\_BFGS\< FunctionType \>::Function () const` [inline]` Return the function that is being optimized. Definition at line 113 of file lbfgs.hpp. ### template\ FunctionType& mlpack::optimization::L\_BFGS\< FunctionType \>::Function ()` [inline]` Modify the function that is being optimized. Definition at line 115 of file lbfgs.hpp. ### template\ bool mlpack::optimization::L\_BFGS\< FunctionType \>::GradientNormTooSmall (const arma::mat &gradient)` [private]` Check to make sure that the norm of the gradient is not smaller than 1e-5. Currently that value is not configurable. **Returns:** (norm \< minGradientNorm). ### template\ bool mlpack::optimization::L\_BFGS\< FunctionType \>::LineSearch (double &functionValue, arma::mat &iterate, arma::mat &gradient, const arma::mat &searchDirection)` [private]` Perform a back-tracking line search along the search direction to calculate a step size satisfying the Wolfe conditions. The parameter iterate will be modified if the method is successful. **Parameters:** *functionValue* Value of the function at the initial point \ *iterate* The initial point to begin the line search from \ *gradient* The gradient at the initial point \ *searchDirection* A vector specifying the search direction \ *stepSize* Variable the calculated step size will be stored in **Returns:** false if no step size is suitable, true otherwise. ### template\ size\_t mlpack::optimization::L\_BFGS\< FunctionType \>::MaxIterations () const` [inline]` Get the maximum number of iterations. Definition at line 123 of file lbfgs.hpp. ### template\ size\_t& mlpack::optimization::L\_BFGS\< FunctionType \>::MaxIterations ()` [inline]` Modify the maximum number of iterations. Definition at line 125 of file lbfgs.hpp. ### template\ size\_t mlpack::optimization::L\_BFGS\< FunctionType \>::MaxLineSearchTrials () const` [inline]` Get the maximum number of line search trials. Definition at line 143 of file lbfgs.hpp. ### template\ size\_t& mlpack::optimization::L\_BFGS\< FunctionType \>::MaxLineSearchTrials ()` [inline]` Modify the maximum number of line search trials. Definition at line 145 of file lbfgs.hpp. ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::MaxStep () const` [inline]` Return the maximum line search step size. Definition at line 153 of file lbfgs.hpp. ### template\ double& mlpack::optimization::L\_BFGS\< FunctionType \>::MaxStep ()` [inline]` Modify the maximum line search step size. Definition at line 155 of file lbfgs.hpp. ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::MinGradientNorm () const` [inline]` Get the minimum gradient norm. Definition at line 138 of file lbfgs.hpp. ### template\ double& mlpack::optimization::L\_BFGS\< FunctionType \>::MinGradientNorm ()` [inline]` Modify the minimum gradient norm. Definition at line 140 of file lbfgs.hpp. ### template\ const std::pair\& mlpack::optimization::L\_BFGS\< FunctionType \>::MinPointIterate () const Return the point where the lowest function value has been found. **Returns:** arma::vec representing the point and a double with the function value at that point. ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::MinStep () const` [inline]` Return the minimum line search step size. Definition at line 148 of file lbfgs.hpp. ### template\ double& mlpack::optimization::L\_BFGS\< FunctionType \>::MinStep ()` [inline]` Modify the minimum line search step size. Definition at line 150 of file lbfgs.hpp. ### template\ size\_t mlpack::optimization::L\_BFGS\< FunctionType \>::NumBasis () const` [inline]` Get the memory size. Definition at line 118 of file lbfgs.hpp. ### template\ size\_t& mlpack::optimization::L\_BFGS\< FunctionType \>::NumBasis ()` [inline]` Modify the memory size. Definition at line 120 of file lbfgs.hpp. ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::Optimize (arma::mat &iterate) Use L-BFGS to optimize the given function, starting at the given iterate point and finding the minimum. The maximum number of iterations is set in the constructor (or with **MaxIterations()**). Alternately, another overload is provided which takes a maximum number of iterations as a parameter. The given starting point will be modified to store the finishing point of the algorithm, and the final objective value is returned. **Parameters:** *iterate* Starting point (will be modified). **Returns:** Objective value of the final point. ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::Optimize (arma::mat &iterate, const size\_tmaxIterations) Use L-BFGS to optimize (minimize) the given function, starting at the given iterate point, and performing no more than the given maximum number of iterations (the class variable maxIterations is ignored for this run, but not modified). The given starting point will be modified to store the finishing point of the algorithm, and the final objective value is returned. **Parameters:** *iterate* Starting point (will be modified). \ *maxIterations* Maximum number of iterations (0 specifies no limit). **Returns:** Objective value of the final point. ### template\ void mlpack::optimization::L\_BFGS\< FunctionType \>::SearchDirection (const arma::mat &gradient, const size\_titerationNum, const doublescalingFactor, arma::mat &searchDirection)` [private]` Find the L-BFGS search direction. **Parameters:** *gradient* The gradient at the current point \ *iteration\_num* The iteration number \ *scaling\_factor* Scaling factor to use (see ChooseScalingFactor\_()) \ *search\_direction* Vector to store search direction in ### template\ std::string mlpack::optimization::L\_BFGS\< FunctionType \>::ToString () const ### template\ void mlpack::optimization::L\_BFGS\< FunctionType \>::UpdateBasisSet (const size\_titerationNum, const arma::mat &iterate, const arma::mat &oldIterate, const arma::mat &gradient, const arma::mat &oldGradient)` [private]` Update the y and s matrices, which store the differences between the iterate and old iterate and the differences between the gradient and the old gradient, respectively. **Parameters:** *iterationNum* Iteration number \ *iterate* Current point \ *oldIterate* Point at last iteration \ *gradient* Gradient at current point (iterate) \ *oldGradient* Gradient at last iteration point (oldIterate) ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::Wolfe () const` [inline]` Get the Wolfe parameter. Definition at line 133 of file lbfgs.hpp. ### template\ double& mlpack::optimization::L\_BFGS\< FunctionType \>::Wolfe ()` [inline]` Modify the Wolfe parameter. Definition at line 135 of file lbfgs.hpp. ## Member Data Documentation ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::armijoConstant` [private]` Parameter for determining the Armijo condition. Definition at line 176 of file lbfgs.hpp. Referenced by mlpack::optimization::L\_BFGS\< AugLagrangianFunction\< mlpack::optimization::LRSDPFunction \> \>::ArmijoConstant(). ### template\ FunctionType& mlpack::optimization::L\_BFGS\< FunctionType \>::function` [private]` Internal reference to the function we are optimizing. Definition at line 162 of file lbfgs.hpp. ### template\ size\_t mlpack::optimization::L\_BFGS\< FunctionType \>::maxIterations` [private]` Maximum number of iterations. Definition at line 174 of file lbfgs.hpp. Referenced by mlpack::optimization::L\_BFGS\< AugLagrangianFunction\< mlpack::optimization::LRSDPFunction \> \>::MaxIterations(). ### template\ size\_t mlpack::optimization::L\_BFGS\< FunctionType \>::maxLineSearchTrials` [private]` Maximum number of trials for the line search. Definition at line 182 of file lbfgs.hpp. Referenced by mlpack::optimization::L\_BFGS\< AugLagrangianFunction\< mlpack::optimization::LRSDPFunction \> \>::MaxLineSearchTrials(). ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::maxStep` [private]` Maximum step of the line search. Definition at line 186 of file lbfgs.hpp. Referenced by mlpack::optimization::L\_BFGS\< AugLagrangianFunction\< mlpack::optimization::LRSDPFunction \> \>::MaxStep(). ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::minGradientNorm` [private]` Minimum gradient norm required to continue the optimization. Definition at line 180 of file lbfgs.hpp. Referenced by mlpack::optimization::L\_BFGS\< AugLagrangianFunction\< mlpack::optimization::LRSDPFunction \> \>::MinGradientNorm(). ### template\ std::pair\ mlpack::optimization::L\_BFGS\< FunctionType \>::minPointIterate` [private]` Best point found so far. Definition at line 189 of file lbfgs.hpp. ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::minStep` [private]` Minimum step of the line search. Definition at line 184 of file lbfgs.hpp. Referenced by mlpack::optimization::L\_BFGS\< AugLagrangianFunction\< mlpack::optimization::LRSDPFunction \> \>::MinStep(). ### template\ arma::mat mlpack::optimization::L\_BFGS\< FunctionType \>::newIterateTmp` [private]` Position of the new iterate. Definition at line 165 of file lbfgs.hpp. ### template\ size\_t mlpack::optimization::L\_BFGS\< FunctionType \>::numBasis` [private]` Size of memory for this L-BFGS optimizer. Definition at line 172 of file lbfgs.hpp. Referenced by mlpack::optimization::L\_BFGS\< AugLagrangianFunction\< mlpack::optimization::LRSDPFunction \> \>::NumBasis(). ### template\ arma::cube mlpack::optimization::L\_BFGS\< FunctionType \>::s` [private]` Stores all the s matrices in memory. Definition at line 167 of file lbfgs.hpp. ### template\ double mlpack::optimization::L\_BFGS\< FunctionType \>::wolfe` [private]` Parameter for detecting the Wolfe condition. Definition at line 178 of file lbfgs.hpp. Referenced by mlpack::optimization::L\_BFGS\< AugLagrangianFunction\< mlpack::optimization::LRSDPFunction \> \>::Wolfe(). ### template\ arma::cube mlpack::optimization::L\_BFGS\< FunctionType \>::y` [private]` Stores all the y matrices in memory. Definition at line 169 of file lbfgs.hpp. ## Author Generated automatically by Doxygen for MLPACK from the source code.