# Ipopt::LowRankAugSystemSolver Class Reference

Solver for the augmented system with LowRankUpdateSymMatrix Hessian matrices. More...

`#include <IpLowRankAugSystemSolver.hpp>`

Inheritance diagram for Ipopt::LowRankAugSystemSolver:
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List of all members.

## Public Member Functions
bool | InitializeImpl (const OptionsList &options, const std::string &prefix)
| overloaded from AlgorithmStrategyObject
virtual ESymSolverStatus | Solve (const SymMatrix *W, double W_factor, const Vector *D_x, double delta_x, const Vector *D_s, double delta_s, const Matrix *J_c, const Vector *D_c, double delta_c, const Matrix *J_d, const Vector *D_d, double delta_d, const Vector &rhs_x, const Vector &rhs_s, const Vector &rhs_c, const Vector &rhs_d, Vector &sol_x, Vector &sol_s, Vector &sol_c, Vector &sol_d, bool check_NegEVals, Index numberOfNegEVals)
| Set up the augmented system and solve it for a given right hand side.
virtual Index | NumberOfNegEVals () const
| Number of negative eigenvalues detected during last solve.
virtual bool | ProvidesInertia () const
| Query whether inertia is computed by linear solver.
virtual bool | IncreaseQuality ()
| Request to increase quality of solution for next solve.
Constructors/Destructors
| LowRankAugSystemSolver (AugSystemSolver &aug_system_solver)
| Constructor using only a linear solver object.
virtual | ~LowRankAugSystemSolver ()
| Default destructor.
## Private Member Functions
Default Compiler Generated Methods
(Hidden to avoid implicit creation/calling). These methods are not implemented and we do not want the compiler to implement them for us, so we declare them private and do not define them. This ensures that they will not be implicitly created/called.
| LowRankAugSystemSolver ()
| Default constructor.
| LowRankAugSystemSolver (const LowRankAugSystemSolver &)
| Copy Constructor.
void | operator= (const LowRankAugSystemSolver &)
| Overloaded Equals Operator.
Internal functions
ESymSolverStatus | UpdateFactorization (const SymMatrix *W, double W_factor, const Vector *D_x, double delta_x, const Vector *D_s, double delta_s, const Matrix &J_c, const Vector *D_c, double delta_c, const Matrix &J_d, const Vector *D_d, double delta_d, const Vector &proto_rhs_x, const Vector &proto_rhs_s, const Vector &proto_rhs_c, const Vector &proto_rhs_d, bool check_NegEVals, Index numberOfNegEVals)
| Method for updating the factorization, including J1_, J2_, Vtilde1_, Utilde2, Wdiag_, compound_sol_vecspace_.
ESymSolverStatus | SolveMultiVector (const Vector *D_x, double delta_x, const Vector *D_s, double delta_s, const Matrix &J_c, const Vector *D_c, double delta_c, const Matrix &J_d, const Vector *D_d, double delta_d, const Vector &proto_rhs_x, const Vector &proto_rhs_s, const Vector &proto_rhs_c, const Vector &proto_rhs_d, const MultiVectorMatrix &V, const SmartPtr< const Matrix > &P_LM, SmartPtr< MultiVectorMatrix > &V_x, SmartPtr< MultiVectorMatrix > &Vtilde1, SmartPtr< MultiVectorMatrix > &Vtilde1_x, bool check_NegEVals, Index numberOfNegEVals)
| Method for solving the augmented system without low-rank update for multiple right hand sides that are provided as MultiVectorMatrix.
bool | AugmentedSystemRequiresChange (const SymMatrix *W, double W_factor, const Vector *D_x, double delta_x, const Vector *D_s, double delta_s, const Matrix &J_c, const Vector *D_c, double delta_c, const Matrix &J_d, const Vector *D_d, double delta_d)
| Method that compares the tags of the data for the matrix with those from the previous call.
## Private Attributes
SmartPtr< AugSystemSolver > | aug_system_solver_
| The augmented system solver object that should be used for the factorization of the augmented system without the low-rank update.
Index | num_neg_evals_
| Stores the number of negative eigenvalues detected during most recent factorization.
Tags and values to track in order to decide whether the
matrix has to be updated compared to the most recent call of the Set method.
TaggedObject::Tag | w_tag_
| Tag for W matrix.
double | w_factor_
| Most recent value of W_factor.
TaggedObject::Tag | d_x_tag_
| Tag for D_x vector, representing the diagonal matrix D_x.
double | delta_x_
| Most recent value of delta_x from Set method.
TaggedObject::Tag | d_s_tag_
| Tag for D_s vector, representing the diagonal matrix D_s.
double | delta_s_
| Most recent value of delta_s from Set method.
TaggedObject::Tag | j_c_tag_
| Tag for J_c matrix.
TaggedObject::Tag | d_c_tag_
| Tag for D_c vector, representing the diagonal matrix D_c.
double | delta_c_
| Most recent value of delta_c from Set method.
TaggedObject::Tag | j_d_tag_
| Tag for J_d matrix.
TaggedObject::Tag | d_d_tag_
| Tag for D_d vector, representing the diagonal matrix D_d.
double | delta_d_
| Most recent value of delta_d from Set method.
Information to be stored in order to resolve for the
same matrix with a different right hand side.
bool | first_call_
SmartPtr< DenseGenMatrix > | J1_
SmartPtr< DenseGenMatrix > | J2_
SmartPtr< MultiVectorMatrix > | Vtilde1_
SmartPtr< MultiVectorMatrix > | Utilde2_
SmartPtr< DiagMatrix > | Wdiag_
| Hessian Matrix passed to the augmented system solver solving the matrix without the low-rank update.
SmartPtr< const CompoundVectorSpace > | compound_sol_vecspace_
| Vector space for Compound vectors that capture the entire right hand side and solution vectors .

## Detailed Description

Solver for the augmented system with LowRankUpdateSymMatrix Hessian matrices.

This version works with the Sherman-Morrison formula and multiple backsolves.

Definition at line 24 of file IpLowRankAugSystemSolver.hpp.

## Constructor & Destructor Documentation

Ipopt::LowRankAugSystemSolver::LowRankAugSystemSolver | ( | AugSystemSolver & | aug_system_solver | ) |

Constructor using only a linear solver object.

virtual Ipopt::LowRankAugSystemSolver::~LowRankAugSystemSolver | ( |  | ) | `[virtual]`

Default destructor.

Ipopt::LowRankAugSystemSolver::LowRankAugSystemSolver | ( |  | ) | `[private]`

Default constructor.

Ipopt::LowRankAugSystemSolver::LowRankAugSystemSolver | ( | const LowRankAugSystemSolver & |  | ) | `[private]`

Copy Constructor.

## Member Function Documentation

bool Ipopt::LowRankAugSystemSolver::InitializeImpl | ( | const OptionsList & | options,
|  | const std::string & | prefix |
| ) |  |  | `[virtual]`

overloaded from AlgorithmStrategyObject

Implements Ipopt::AugSystemSolver.

virtual ESymSolverStatus Ipopt::LowRankAugSystemSolver::Solve | ( | const SymMatrix * | W,
|  | double | W_factor,
|  | const Vector * | D_x,
|  | double | delta_x,
|  | const Vector * | D_s,
|  | double | delta_s,
|  | const Matrix * | J_c,
|  | const Vector * | D_c,
|  | double | delta_c,
|  | const Matrix * | J_d,
|  | const Vector * | D_d,
|  | double | delta_d,
|  | const Vector & | rhs_x,
|  | const Vector & | rhs_s,
|  | const Vector & | rhs_c,
|  | const Vector & | rhs_d,
|  | Vector & | sol_x,
|  | Vector & | sol_s,
|  | Vector & | sol_c,
|  | Vector & | sol_d,
|  | bool | check_NegEVals,
|  | Index | numberOfNegEVals |
| ) |  |  | `[virtual]`

Set up the augmented system and solve it for a given right hand side.

Reimplemented from Ipopt::AugSystemSolver.

virtual Index Ipopt::LowRankAugSystemSolver::NumberOfNegEVals | ( |  | ) | const`[virtual]`

Number of negative eigenvalues detected during last solve.

Returns the number of negative eigenvalues of the most recent factorized matrix. This must not be called if the linear solver does not compute this quantities (see ProvidesInertia).

Implements Ipopt::AugSystemSolver.

virtual bool Ipopt::LowRankAugSystemSolver::ProvidesInertia | ( |  | ) | const`[virtual]`

Query whether inertia is computed by linear solver.

Returns true, if linear solver provides inertia.

Implements Ipopt::AugSystemSolver.

virtual bool Ipopt::LowRankAugSystemSolver::IncreaseQuality | ( |  | ) | `[virtual]`

Request to increase quality of solution for next solve.

Ask underlying linear solver to increase quality of solution for the next solve (e.g. increase pivot tolerance). Returns false, if this is not possible (e.g. maximal pivot tolerance already used.)

Implements Ipopt::AugSystemSolver.

void Ipopt::LowRankAugSystemSolver::operator= | ( | const LowRankAugSystemSolver & |  | ) | `[private]`

Overloaded Equals Operator.

Reimplemented from Ipopt::AugSystemSolver.

ESymSolverStatus Ipopt::LowRankAugSystemSolver::UpdateFactorization | ( | const SymMatrix * | W,
|  | double | W_factor,
|  | const Vector * | D_x,
|  | double | delta_x,
|  | const Vector * | D_s,
|  | double | delta_s,
|  | const Matrix & | J_c,
|  | const Vector * | D_c,
|  | double | delta_c,
|  | const Matrix & | J_d,
|  | const Vector * | D_d,
|  | double | delta_d,
|  | const Vector & | proto_rhs_x,
|  | const Vector & | proto_rhs_s,
|  | const Vector & | proto_rhs_c,
|  | const Vector & | proto_rhs_d,
|  | bool | check_NegEVals,
|  | Index | numberOfNegEVals |
| ) |  |  | `[private]`

Method for updating the factorization, including J1_, J2_, Vtilde1_, Utilde2, Wdiag_, compound_sol_vecspace_.

ESymSolverStatus Ipopt::LowRankAugSystemSolver::SolveMultiVector | ( | const Vector * | D_x,
|  | double | delta_x,
|  | const Vector * | D_s,
|  | double | delta_s,
|  | const Matrix & | J_c,
|  | const Vector * | D_c,
|  | double | delta_c,
|  | const Matrix & | J_d,
|  | const Vector * | D_d,
|  | double | delta_d,
|  | const Vector & | proto_rhs_x,
|  | const Vector & | proto_rhs_s,
|  | const Vector & | proto_rhs_c,
|  | const Vector & | proto_rhs_d,
|  | const MultiVectorMatrix & | V,
|  | const SmartPtr< const Matrix > & | P_LM,
|  | SmartPtr< MultiVectorMatrix > & | V_x,
|  | SmartPtr< MultiVectorMatrix > & | Vtilde1,
|  | SmartPtr< MultiVectorMatrix > & | Vtilde1_x,
|  | bool | check_NegEVals,
|  | Index | numberOfNegEVals |
| ) |  |  | `[private]`

Method for solving the augmented system without low-rank update for multiple right hand sides that are provided as MultiVectorMatrix.

The result is returned as a MultiVectorMatrix in Vtilde1. V_x and Vtilde1_x are V and Vtilde1 in the x-space.

bool Ipopt::LowRankAugSystemSolver::AugmentedSystemRequiresChange | ( | const SymMatrix * | W,
|  | double | W_factor,
|  | const Vector * | D_x,
|  | double | delta_x,
|  | const Vector * | D_s,
|  | double | delta_s,
|  | const Matrix & | J_c,
|  | const Vector * | D_c,
|  | double | delta_c,
|  | const Matrix & | J_d,
|  | const Vector * | D_d,
|  | double | delta_d |
| ) |  |  | `[private]`

Method that compares the tags of the data for the matrix with those from the previous call.

Returns true, if there was a change and the factorization has to be updated.

## Member Data Documentation

SmartPtr<AugSystemSolver> Ipopt::LowRankAugSystemSolver::aug_system_solver_`[private]`

The augmented system solver object that should be used for the factorization of the augmented system without the low-rank update.

Definition at line 110 of file IpLowRankAugSystemSolver.hpp.

TaggedObject::Tag Ipopt::LowRankAugSystemSolver::w_tag_`[private]`

Tag for W matrix.

If W has been given to Set as NULL, then this tag is set to 0

Definition at line 120 of file IpLowRankAugSystemSolver.hpp.

double Ipopt::LowRankAugSystemSolver::w_factor_`[private]`

Most recent value of W_factor.

Definition at line 122 of file IpLowRankAugSystemSolver.hpp.

TaggedObject::Tag Ipopt::LowRankAugSystemSolver::d_x_tag_`[private]`

Tag for D_x vector, representing the diagonal matrix D_x.

If D_x has been given to Set as NULL, then this tag is set to 0

Definition at line 126 of file IpLowRankAugSystemSolver.hpp.

double Ipopt::LowRankAugSystemSolver::delta_x_`[private]`

Most recent value of delta_x from Set method.

Definition at line 128 of file IpLowRankAugSystemSolver.hpp.

TaggedObject::Tag Ipopt::LowRankAugSystemSolver::d_s_tag_`[private]`

Tag for D_s vector, representing the diagonal matrix D_s.

If D_s has been given to Set as NULL, then this tag is set to 0

Definition at line 132 of file IpLowRankAugSystemSolver.hpp.

double Ipopt::LowRankAugSystemSolver::delta_s_`[private]`

Most recent value of delta_s from Set method.

Definition at line 134 of file IpLowRankAugSystemSolver.hpp.

TaggedObject::Tag Ipopt::LowRankAugSystemSolver::j_c_tag_`[private]`

Tag for J_c matrix.

If J_c has been given to Set as NULL, then this tag is set to 0

Definition at line 138 of file IpLowRankAugSystemSolver.hpp.

TaggedObject::Tag Ipopt::LowRankAugSystemSolver::d_c_tag_`[private]`

Tag for D_c vector, representing the diagonal matrix D_c.

If D_c has been given to Set as NULL, then this tag is set to 0

Definition at line 142 of file IpLowRankAugSystemSolver.hpp.

double Ipopt::LowRankAugSystemSolver::delta_c_`[private]`

Most recent value of delta_c from Set method.

Definition at line 144 of file IpLowRankAugSystemSolver.hpp.

TaggedObject::Tag Ipopt::LowRankAugSystemSolver::j_d_tag_`[private]`

Tag for J_d matrix.

If J_d has been given to Set as NULL, then this tag is set to 0

Definition at line 148 of file IpLowRankAugSystemSolver.hpp.

TaggedObject::Tag Ipopt::LowRankAugSystemSolver::d_d_tag_`[private]`

Tag for D_d vector, representing the diagonal matrix D_d.

If D_d has been given to Set as NULL, then this tag is set to 0

Definition at line 152 of file IpLowRankAugSystemSolver.hpp.

double Ipopt::LowRankAugSystemSolver::delta_d_`[private]`

Most recent value of delta_d from Set method.

Definition at line 154 of file IpLowRankAugSystemSolver.hpp.

bool Ipopt::LowRankAugSystemSolver::first_call_`[private]`

Definition at line 160 of file IpLowRankAugSystemSolver.hpp.

SmartPtr<DenseGenMatrix> Ipopt::LowRankAugSystemSolver::J1_`[private]`

Definition at line 161 of file IpLowRankAugSystemSolver.hpp.

SmartPtr<DenseGenMatrix> Ipopt::LowRankAugSystemSolver::J2_`[private]`

Definition at line 162 of file IpLowRankAugSystemSolver.hpp.

SmartPtr<MultiVectorMatrix> Ipopt::LowRankAugSystemSolver::Vtilde1_`[private]`

Definition at line 163 of file IpLowRankAugSystemSolver.hpp.

SmartPtr<MultiVectorMatrix> Ipopt::LowRankAugSystemSolver::Utilde2_`[private]`

Definition at line 164 of file IpLowRankAugSystemSolver.hpp.

SmartPtr<DiagMatrix> Ipopt::LowRankAugSystemSolver::Wdiag_`[private]`

Hessian Matrix passed to the augmented system solver solving the matrix without the low-rank update.

Definition at line 167 of file IpLowRankAugSystemSolver.hpp.

SmartPtr<const CompoundVectorSpace> Ipopt::LowRankAugSystemSolver::compound_sol_vecspace_`[private]`

Vector space for Compound vectors that capture the entire right hand side and solution vectors .

Definition at line 170 of file IpLowRankAugSystemSolver.hpp.

Index Ipopt::LowRankAugSystemSolver::num_neg_evals_`[private]`

Stores the number of negative eigenvalues detected during most recent factorization.

This is what is returned by NumberOfNegEVals() of this class. It usually is the number of negative eigenvalues retured from the aug_system_solver solve, but if a Cholesky factorization could not be performed, the returned value is one more than this what the aug_system_solver returned.

Definition at line 180 of file IpLowRankAugSystemSolver.hpp.

The documentation for this class was generated from the following file:

- src/Algorithm/IpLowRankAugSystemSolver.hpp

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