ipo::detail Namespace Reference

Namespace for classes that handle details of interior-point optimisation that are not ordinarily accessed directly to set up and solve a convex optimisation problem. More...

Classes
class	BarrierFunction
	Function for the logarithmic barrier. More...
class	LineSearch
	Backtracking line search. More...
class	ModelBase
	Abstract base class for model. More...
class	ModelFunction
	Abstract base class for Objective and Constraint. More...
class	NewtonDescent
	Newton descent method. More...
class	PhaseIModel
	Model used for finding an initial feasible solution in phase I of interior-pont optimisation. More...
class	SharedFunctionPtr
	Shared pointer to ipo::Function object. More...
class	Var
	Abstract base class for Variable and Array;. More...

Functions
std::tuple< gsl::matrix, double >	modifiedCholeskyDecomp (gsl::matrix const &matrix, double maxoffl)
	Modified in-place Cholesky decomposition using the method of Gill, Murray and Wright (1981) to deal with cases where matrix is not positive definite. More...
gsl::matrix	modelHessian (gsl::matrix &matrix)
	Find a Cholesky decomposition (both upper and lower triangles returned in matrix) of a matrix + mu * I, where matrix is a Hessian (assumed symmetric) matrix and mu is chosen to ensure that matrix + mu * I is safely poitive definite and is zero if matrix is already safely positive definite. More...

Detailed Description

Namespace for classes that handle details of interior-point optimisation that are not ordinarily accessed directly to set up and solve a convex optimisation problem.

Function Documentation

gsl::matrix ipo::detail::modelHessian

(

gsl::matrix &

matrix

)

Find a Cholesky decomposition (both upper and lower triangles returned in matrix) of a matrix + mu * I, where matrix is a Hessian (assumed symmetric) matrix and mu is chosen to ensure that matrix + mu * I is safely poitive definite and is zero if matrix is already safely positive definite.

In the algorithm matrix is modified to matrix + mu * I. See Dennis and Schnabel, 1996, Algorithm A.5.5.1.

Parameters

matrix

The Hessian

Returns

matrix The Hessian, possibly with mu * I added

The Cholesky decomposition (as a symmetric matrix, with both upper and lower triangles)

Definition at line 102 of file GSL.cc.

References ipo::format::infinity, and modifiedCholeskyDecomp().

Referenced by ipo::detail::NewtonDescent::operator()().

std::tuple< gsl::matrix, double > ipo::detail::modifiedCholeskyDecomp	(	gsl::matrix const &	matrix,
		double	maxoffl
	)

Modified in-place Cholesky decomposition using the method of Gill, Murray and Wright (1981) to deal with cases where matrix is not positive definite.

See Dennis and Schnabel, 1996: Algorithm A.5.5.2.

This should not be used directly but through modelHessian()

Parameters

matrix	The matrix (assumed symmetric) to decompose in place
maxoffl	A parameter generated by modelHessian

Returns

Cholesky decomoposition (in lower triangle) and maximum of diagonal

Definition at line 29 of file GSL.cc.

References ipo::format::infinity.

Referenced by modelHessian().