--- name: "mlpack_optimization_LRSDP" 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_LRSDP" --- # mlpack\_optimization\_LRSDP(3) LRSDP is the implementation of Monteiro and Burer's formulation of low-rank semidefinite programs (LR-SDP). ## NAME mlpack::optimization::LRSDP - **LRSDP** is the implementation of Monteiro and Burer's formulation of low-rank semidefinite programs (LR-SDP). ## SYNOPSIS ### Public Member Functions **LRSDP** (const size\_t numConstraints, const arma::mat &initialPoint)\ *Create an* **LRSDP** *to be optimized.* **LRSDP** (const size\_t numConstraints, const arma::mat &initialPoint, **AugLagrangian**\< **LRSDPFunction** \> &augLagrangian)\ *Create an* **LRSDP** *to be optimized, passing in an already-created* **AugLagrangian** *object.* const std::vector\< arma::mat \> & **A** () const \ *Return the vector of A matrices (which correspond to the constraints).* std::vector\< arma::mat \> & **A** ()\ *Modify the veector of A matrices (which correspond to the constraints).* const arma::uvec & **AModes** () const \ *Return the vector of modes for the A matrices.* arma::uvec & **AModes** ()\ *Modify the vector of modes for the A matrices.* const **AugLagrangian**\ \< **LRSDPFunction** \> & **AugLag** () const "\ *Return the augmented Lagrangian object.* **AugLagrangian**\< **LRSDPFunction** \> & **AugLag** ()\ *Modify the augmented Lagrangian object.* const arma::vec & **B** () const \ *Return the vector of B values.* arma::vec & **B** ()\ *Modify the vector of B values.* const arma::mat & **C** () const \ *Return the objective function matrix (C).* arma::mat & **C** ()\ *Modify the objective function matrix (C).* const **LRSDPFunction** & **Function** () const \ *Return the function to be optimized.* **LRSDPFunction** & **Function** ()\ *Modify the function to be optimized.* double **Optimize** (arma::mat &coordinates)\ *Optimize the* **LRSDP** *and return the final objective value.* std::string **ToString** () const \ *Return a string representation of the object.* ### Private Attributes **AugLagrangian**\< **LRSDPFunction** \> **augLag**\ *The* **AugLagrangian** *object which will be used for optimization.* **LRSDPFunction** **function**\ *Function to optimize, which the* **AugLagrangian** *object holds.* ## Detailed Description **LRSDP** is the implementation of Monteiro and Burer's formulation of low-rank semidefinite programs (LR-SDP). This solver uses the augmented Lagrangian optimizer to solve low-rank semidefinite programs. Definition at line 39 of file lrsdp.hpp. ## Constructor & Destructor Documentation ### mlpack::optimization::LRSDP::LRSDP (const size\_tnumConstraints, const arma::mat &initialPoint) Create an **LRSDP** to be optimized. The solution will end up being a matrix of size (rank) x (rows). To construct each constraint and the objective function, use the functions **A()**, **B()**, and **C()** to set them correctly. **Parameters:** *numConstraints* Number of constraints in the problem. \ *rank* Rank of the solution (\<= rows). \ *rows* Number of rows in the solution. ### mlpack::optimization::LRSDP::LRSDP (const size\_tnumConstraints, const arma::mat &initialPoint, AugLagrangian\< LRSDPFunction \> &augLagrangian) Create an **LRSDP** to be optimized, passing in an already-created **AugLagrangian** object. The given initial point should be set to the size (rows) x (rank), where (rank) is the reduced rank of the problem. **Parameters:** *numConstraints* Number of constraints in the problem. \ *initialPoint* Initial point of the optimization. \ *auglag* Pre-initialized AugLagrangian\ object. ## Member Function Documentation ### const std::vector\& mlpack::optimization::LRSDP::A () const` [inline]` Return the vector of A matrices (which correspond to the constraints). Definition at line 81 of file lrsdp.hpp. ### std::vector\& mlpack::optimization::LRSDP::A ()` [inline]` Modify the veector of A matrices (which correspond to the constraints). Definition at line 83 of file lrsdp.hpp. ### const arma::uvec& mlpack::optimization::LRSDP::AModes () const` [inline]` Return the vector of modes for the A matrices. Definition at line 86 of file lrsdp.hpp. ### arma::uvec& mlpack::optimization::LRSDP::AModes ()` [inline]` Modify the vector of modes for the A matrices. Definition at line 88 of file lrsdp.hpp. ### const AugLagrangian\& mlpack::optimization::LRSDP::AugLag () const` [inline]` Return the augmented Lagrangian object. Definition at line 101 of file lrsdp.hpp. References augLag. ### AugLagrangian\& mlpack::optimization::LRSDP::AugLag ()` [inline]` Modify the augmented Lagrangian object. Definition at line 103 of file lrsdp.hpp. References augLag. ### const arma::vec& mlpack::optimization::LRSDP::B () const` [inline]` Return the vector of B values. Definition at line 91 of file lrsdp.hpp. ### arma::vec& mlpack::optimization::LRSDP::B ()` [inline]` Modify the vector of B values. Definition at line 93 of file lrsdp.hpp. ### const arma::mat& mlpack::optimization::LRSDP::C () const` [inline]` Return the objective function matrix (C). Definition at line 76 of file lrsdp.hpp. ### arma::mat& mlpack::optimization::LRSDP::C ()` [inline]` Modify the objective function matrix (C). Definition at line 78 of file lrsdp.hpp. ### const LRSDPFunction& mlpack::optimization::LRSDP::Function () const` [inline]` Return the function to be optimized. Definition at line 96 of file lrsdp.hpp. ### LRSDPFunction& mlpack::optimization::LRSDP::Function ()` [inline]` Modify the function to be optimized. Definition at line 98 of file lrsdp.hpp. ### double mlpack::optimization::LRSDP::Optimize (arma::mat &coordinates) Optimize the **LRSDP** and return the final objective value. The given coordinates will be modified to contain the final solution. **Parameters:** *coordinates* Starting coordinates for the optimization. ### std::string mlpack::optimization::LRSDP::ToString () const Return a string representation of the object. ## Member Data Documentation ### AugLagrangian\ mlpack::optimization::LRSDP::augLag` [private]` The **AugLagrangian** object which will be used for optimization. Definition at line 113 of file lrsdp.hpp. Referenced by AugLag(). ### LRSDPFunction mlpack::optimization::LRSDP::function` [private]` Function to optimize, which the **AugLagrangian** object holds. Definition at line 110 of file lrsdp.hpp. ## Author Generated automatically by Doxygen for MLPACK from the source code.