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

#include <ROL_ScalarLinearEqualityConstraint.hpp>

Inheritance diagram for ROL::ScalarLinearEqualityConstraint< Real >:

Public Member Functions
	ScalarLinearEqualityConstraint (const Teuchos::RCP< Vector< Real > > &a, const Real b)

void	value (Vector< Real > &c, const Vector< Real > &x, Real &tol)
	Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\). More...

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 \(v\). More...

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 \(v\). More...

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 \( v \mapsto c''(x)(v,\cdot)^*u \). More...

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 \[ \begin{pmatrix} I & c'(x)^* \\ c'(x) & 0 \end{pmatrix} \begin{pmatrix} v_{1} \\ v_{2} \end{pmatrix} = \begin{pmatrix} b_{1} \\ b_{2} \end{pmatrix} \] where \(v_{1} \in \mathcal{X}\), \(v_{2} \in \mathcal{C}^\), \(b_{1} \in \mathcal{X}^\), \(b_{2} \in \mathcal{C}\), \(I : \mathcal{X} \rightarrow \mathcal{X}^\) is an identity or Riesz operator, and \(0 : \mathcal{C}^ \rightarrow \mathcal{C}\) is a zero operator. More...

Public Member Functions inherited from ROL::EqualityConstraint< Real >
virtual	~EqualityConstraint ()

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 \(v\). More...

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: \[ \left[c'(x) \circ R \circ c'(x)^ \circ P(x)\right] v = v \,, \] where R is the appropriate Riesz map in \(L(\mathcal{X}^*, \mathcal{X})\). It is used by the solveAugmentedSystem method. More...

	EqualityConstraint (void)

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. More...

virtual bool	isFeasible (const Vector< Real > &v)
	Check if the vector, v, is feasible. More...

void	activate (void)
	Turn on constraints. More...

void	deactivate (void)
	Turn off constraints. More...

bool	isActivated (void)
	Check if constraints are on. More...

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. More...

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. More...

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. More...

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. More...

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. More...

virtual void	setParameter (const std::vector< Real > &param)

Private Attributes
const Teuchos::RCP< Vector < Real > >	a_
	Dual vector defining hyperplane. More...

const Real	b_
	Affine shift. More...

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

Detailed Description

template<class Real>
class ROL::ScalarLinearEqualityConstraint< 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::StdVector 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 80 of file ROL_ScalarLinearEqualityConstraint.hpp.

Constructor & Destructor Documentation

template<class Real >

ROL::ScalarLinearEqualityConstraint< Real >::ScalarLinearEqualityConstraint	(	const Teuchos::RCP< Vector< Real > > &	a,
		const Real	b
	)

inline

Definition at line 86 of file ROL_ScalarLinearEqualityConstraint.hpp.

Member Function Documentation

template<class Real >

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

inlinevirtual

Evaluate the constraint operator \(c:\mathcal{X} \rightarrow \mathcal{C}\) at \(x\).

Parameters

[out]	c	is the result of evaluating the constraint operator at x; a constraint-space vector
[in]	x	is the constraint argument; an optimization-space vector
[in,out]	tol	is a tolerance for inexact evaluations; currently unused

On return, \(\mathsf{c} = c(x)\), where \(\mathsf{c} \in \mathcal{C}\), \(\mathsf{x} \in \mathcal{X}\).

Implements ROL::EqualityConstraint< Real >.

Definition at line 90 of file ROL_ScalarLinearEqualityConstraint.hpp.

References ROL::ScalarLinearEqualityConstraint< Real >::a_, ROL::ScalarLinearEqualityConstraint< Real >::b_, ROL::Vector< Real >::dual(), and ROL::StdVector< Real, Element >::getVector().

template<class Real >

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

inlinevirtual

Apply the constraint Jacobian at \(x\), \(c'(x) \in L(\mathcal{X}, \mathcal{C})\), to vector \(v\).

Parameters

[out]	jv	is the result of applying the constraint Jacobian to v at x; a constraint-space vector
[in]	v	is an optimization-space vector
[in]	x	is the constraint argument; an optimization-space vector
[in,out]	tol	is a tolerance for inexact evaluations; currently unused

On return, \(\mathsf{jv} = c'(x)v\), where \(v \in \mathcal{X}\), \(\mathsf{jv} \in \mathcal{C}\).

The default implementation is a finite-difference approximation.

Reimplemented from ROL::EqualityConstraint< Real >.

Definition at line 96 of file ROL_ScalarLinearEqualityConstraint.hpp.

References ROL::ScalarLinearEqualityConstraint< Real >::a_, ROL::Vector< Real >::dual(), and ROL::StdVector< Real, Element >::getVector().

template<class Real >

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

inlinevirtual

Apply the adjoint of the the constraint Jacobian at \(x\), \(c'(x)^* \in L(\mathcal{C}^*, \mathcal{X}^*)\), to vector \(v\).

Parameters

[out]	ajv	is the result of applying the adjoint of the constraint Jacobian to v at x; a dual optimization-space vector
[in]	v	is a dual constraint-space vector
[in]	x	is the constraint argument; an optimization-space vector
[in,out]	tol	is a tolerance for inexact evaluations; currently unused

On return, \(\mathsf{ajv} = c'(x)^*v\), where \(v \in \mathcal{C}^*\), \(\mathsf{ajv} \in \mathcal{X}^*\).

The default implementation is a finite-difference approximation.

Reimplemented from ROL::EqualityConstraint< Real >.

Definition at line 103 of file ROL_ScalarLinearEqualityConstraint.hpp.

References ROL::ScalarLinearEqualityConstraint< Real >::a_, ROL::StdVector< Real, Element >::getVector(), ROL::Vector< Real >::scale(), and ROL::Vector< Real >::set().

template<class Real >

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

inlinevirtual

Apply the derivative of the adjoint of the constraint Jacobian at \(x\) to vector \(u\) in direction \(v\), according to \( v \mapsto c''(x)(v,\cdot)^*u \).

Parameters

[out]	ahuv	is the result of applying the derivative of the adjoint of the constraint Jacobian at x to vector u in direction v; a dual optimization-space vector
[in]	u	is the direction vector; a dual constraint-space vector
[in]	v	is an optimization-space vector
[in]	x	is the constraint argument; an optimization-space vector
[in,out]	tol	is a tolerance for inexact evaluations; currently unused

On return, \( \mathsf{ahuv} = c''(x)(v,\cdot)^*u \), where \(u \in \mathcal{C}^*\), \(v \in \mathcal{X}\), and \(\mathsf{ahuv} \in \mathcal{X}^*\).

The default implementation is a finite-difference approximation based on the adjoint Jacobian.

Reimplemented from ROL::EqualityConstraint< Real >.

Definition at line 111 of file ROL_ScalarLinearEqualityConstraint.hpp.

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

template<class Real >

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

inlinevirtual

Approximately solves the augmented system

\[ \begin{pmatrix} I & c'(x)^* \\ c'(x) & 0 \end{pmatrix} \begin{pmatrix} v_{1} \\ v_{2} \end{pmatrix} = \begin{pmatrix} b_{1} \\ b_{2} \end{pmatrix} \]

where \(v_{1} \in \mathcal{X}\), \(v_{2} \in \mathcal{C}^*\), \(b_{1} \in \mathcal{X}^*\), \(b_{2} \in \mathcal{C}\), \(I : \mathcal{X} \rightarrow \mathcal{X}^*\) is an identity or Riesz operator, and \(0 : \mathcal{C}^* \rightarrow \mathcal{C}\) is a zero operator.

Parameters

[out]	v1	is the optimization-space component of the result
[out]	v2	is the dual constraint-space component of the result
[in]	b1	is the dual optimization-space component of the right-hand side
[in]	b2	is the constraint-space component of the right-hand side
[in]	x	is the constraint argument; an optimization-space vector
[in,out]	tol	is the nominal relative residual tolerance

On return, \( [\mathsf{v1} \,\, \mathsf{v2}] \) approximately solves the augmented system, where the size of the residual is governed by special stopping conditions.

The default implementation is the preconditioned generalized minimal residual (GMRES) method, which enables the use of nonsymmetric preconditioners.

Reimplemented from ROL::EqualityConstraint< Real >.

Definition at line 117 of file ROL_ScalarLinearEqualityConstraint.hpp.

References ROL::ScalarLinearEqualityConstraint< Real >::a_, ROL::Vector< Real >::axpy(), ROL::Vector< Real >::dual(), ROL::StdVector< Real, Element >::getVector(), and ROL::Vector< Real >::set().