This equality constraint defines an affine hyperplane. More...

#include <ROL_ScalarLinearConstraint.hpp>

Inheritance diagram for ROL::ScalarLinearConstraint< Real >:

Public Member Functions
	ScalarLinearConstraint (const Ptr< const Vector< Real > > &a, const Real b)
void	value (Vector< Real > &c, const Vector< Real > &x, Real &tol) override
void	applyJacobian (Vector< Real > &jv, const Vector< Real > &v, const Vector< Real > &x, Real &tol) override
void	applyAdjointJacobian (Vector< Real > &ajv, const Vector< Real > &v, const Vector< Real > &x, Real &tol) override
void	applyAdjointHessian (Vector< Real > &ahuv, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &x, Real &tol) override
std::vector< Real >	solveAugmentedSystem (Vector< Real > &v1, Vector< Real > &v2, const Vector< Real > &b1, const Vector< Real > &b2, const Vector< Real > &x, Real &tol) override
Public Member Functions inherited from ROL::ROL::Constraint< Real >
virtual	~Constraint (void)
	Constraint (void)
virtual void	update (const Vector< Real > &x, UpdateType type, int iter=-1)
	Update constraint function.
virtual void	update (const Vector< Real > &x, bool flag=true, int iter=-1)
	Update constraint functions. x is the optimization variable, flag = true if optimization variable is changed, iter is the outer algorithm iterations count.
virtual void	value (Vector< Real > &c, const Vector< Real > &x, Real &tol)=0
	Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\).
virtual void	applyJacobian (Vector< Real > &jv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply the constraint Jacobian at \(x\), \(c'(x) \in L(\mathcal{X}, \mathcal{C})\), to vector \(v\).
virtual void	applyAdjointJacobian (Vector< Real > &ajv, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply the adjoint of the the constraint Jacobian at \(x\), \(c'(x)^* \in L(\mathcal{C}^, \mathcal{X}^)\), to vector \(v\).
virtual void	applyAdjointJacobian (Vector< Real > &ajv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &dualv, Real &tol)
	Apply the adjoint of the the constraint Jacobian at \(x\), \(c'(x)^* \in L(\mathcal{C}^, \mathcal{X}^)\), to vector \(v\).
virtual void	applyAdjointHessian (Vector< Real > &ahuv, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &x, Real &tol)
	Apply the derivative of the adjoint of the constraint Jacobian at \(x\) to vector \(u\) in direction \(v\), according to \( v \mapsto c''(x)(v,\cdot)^*u \).
virtual std::vector< Real >	solveAugmentedSystem (Vector< Real > &v1, Vector< Real > &v2, const Vector< Real > &b1, const Vector< Real > &b2, const Vector< Real > &x, Real &tol)
	Approximately solves the augmented system .
virtual void	applyPreconditioner (Vector< Real > &pv, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &g, Real &tol)
	Apply a constraint preconditioner at \(x\), \(P(x) \in L(\mathcal{C}, \mathcal{C}^*)\), to vector \(v\). Ideally, this preconditioner satisfies the following relationship:
void	activate (void)
	Turn on constraints.
void	deactivate (void)
	Turn off constraints.
bool	isActivated (void)
	Check if constraints are on.
virtual std::vector< std::vector< Real > >	checkApplyJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &jv, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference check for the constraint Jacobian application.
virtual std::vector< std::vector< Real > >	checkApplyJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &jv, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference check for the constraint Jacobian application.
virtual std::vector< std::vector< Real > >	checkApplyAdjointJacobian (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &c, const Vector< Real > &ajv, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS)
	Finite-difference check for the application of the adjoint of constraint Jacobian.
virtual Real	checkAdjointConsistencyJacobian (const Vector< Real > &w, const Vector< Real > &v, const Vector< Real > &x, const bool printToStream=true, std::ostream &outStream=std::cout)
virtual Real	checkAdjointConsistencyJacobian (const Vector< Real > &w, const Vector< Real > &v, const Vector< Real > &x, const Vector< Real > &dualw, const Vector< Real > &dualv, const bool printToStream=true, std::ostream &outStream=std::cout)
virtual std::vector< std::vector< Real > >	checkApplyAdjointHessian (const Vector< Real > &x, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &hv, const std::vector< Real > &step, const bool printToScreen=true, std::ostream &outStream=std::cout, const int order=1)
	Finite-difference check for the application of the adjoint of constraint Hessian.
virtual std::vector< std::vector< Real > >	checkApplyAdjointHessian (const Vector< Real > &x, const Vector< Real > &u, const Vector< Real > &v, const Vector< Real > &hv, const bool printToScreen=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1)
	Finite-difference check for the application of the adjoint of constraint Hessian.
virtual void	setParameter (const std::vector< Real > &param)

Private Attributes
const Ptr< const Vector< Real > >	a_
	Dual vector defining hyperplane.
const Real	b_
	Affine shift.

Additional Inherited Members
Protected Member Functions inherited from ROL::ROL::Constraint< Real >
const std::vector< Real >	getParameter (void) const

Detailed Description

template<typename Real>
class ROL::ScalarLinearConstraint< Real >

This equality constraint defines an affine hyperplane.

ROL's scalar linear equality constraint interface implements

\[ c(x) := \langle a, x\rangle_{\mathcal{X}^*,\mathcal{X}} - b = 0 \]

where \(a\in\mathcal{X}^*\) and \(b\in\mathbb{R}\). The range space of \(c\) is an ROL::SingletonVector with dimension 1.

Note: If \(a\neq 0\) then there exists an explicit solution of the augmented system. Namely,

\[ v_1 = I^{-1}(b_1-av_2) \quad\text{and}\quad v_2 = \frac{(\langle a,I^{-1}b_1\rangle_{\mathcal{X}^*,\mathcal{X}} - b_2)}{\|a\|_{\mathcal{X}^*}^2}\,. \]

Moreover, note that \(I^{-1}v\) for any \(v\in\mathcal{X}^*\) is implemented in ROL as v.dual().

Definition at line 46 of file ROL_ScalarLinearConstraint.hpp.

Constructor & Destructor Documentation

◆ ScalarLinearConstraint()

template<typename Real>

ROL::ScalarLinearConstraint< Real >::ScalarLinearConstraint	(	const Ptr< const Vector< Real > > &	a,
		const Real	b )

Definition at line 16 of file ROL_ScalarLinearConstraint_Def.hpp.

References a_, and b_.

Member Function Documentation

◆ value()

template<typename Real>

void ROL::ScalarLinearConstraint< Real >::value	(	Vector< Real > &	c,
		const Vector< Real > &	x,
		Real &	tol )

override

Definition at line 21 of file ROL_ScalarLinearConstraint_Def.hpp.

References a_, b_, and ROL::SingletonVector< Real >::setValue().

◆ applyJacobian()

template<typename Real>

void ROL::ScalarLinearConstraint< Real >::applyJacobian	(	Vector< Real > &	jv,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		Real &	tol )

override

Definition at line 28 of file ROL_ScalarLinearConstraint_Def.hpp.

References a_, and ROL::SingletonVector< Real >::setValue().

◆ applyAdjointJacobian()

template<typename Real>

void ROL::ScalarLinearConstraint< Real >::applyAdjointJacobian	(	Vector< Real > &	ajv,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		Real &	tol )

override

Definition at line 37 of file ROL_ScalarLinearConstraint_Def.hpp.

References a_, ROL::SingletonVector< Real >::getValue(), ROL::Vector< Real >::scale(), and ROL::Vector< Real >::set().

◆ applyAdjointHessian()

template<typename Real>

void ROL::ScalarLinearConstraint< Real >::applyAdjointHessian	(	Vector< Real > &	ahuv,
		const Vector< Real > &	u,
		const Vector< Real > &	v,
		const Vector< Real > &	x,
		Real &	tol )

override

Definition at line 46 of file ROL_ScalarLinearConstraint_Def.hpp.

References ROL::Vector< Real >::zero().

◆ solveAugmentedSystem()

template<typename Real>

std::vector< Real > ROL::ScalarLinearConstraint< Real >::solveAugmentedSystem	(	Vector< Real > &	v1,
		Vector< Real > &	v2,
		const Vector< Real > &	b1,
		const Vector< Real > &	b2,
		const Vector< Real > &	x,
		Real &	tol )