Provides the interface to evaluate objective functions. More...
#include <ROL_Constraint_SerialSimOpt.hpp>
Inheritance diagram for ROL::ROL::Objective< Real >:
Public Member Functions | |
| virtual | ~Objective () |
| Objective () | |
| virtual void | update (const Vector< Real > &x, UpdateType type, int iter=-1) |
| Update objective function. | |
| virtual void | update (const Vector< Real > &x, bool flag=true, int iter=-1) |
| Update objective function. | |
| virtual Real | value (const Vector< Real > &x, Real &tol)=0 |
| Compute value. | |
| virtual void | gradient (Vector< Real > &g, const Vector< Real > &x, Real &tol) |
| Compute gradient. | |
| virtual Real | dirDeriv (const Vector< Real > &x, const Vector< Real > &d, Real &tol) |
| Compute directional derivative. | |
| virtual void | hessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol) |
| Apply Hessian approximation to vector. | |
| virtual void | invHessVec (Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &x, Real &tol) |
| Apply inverse Hessian approximation to vector. | |
| virtual void | precond (Vector< Real > &Pv, const Vector< Real > &v, const Vector< Real > &x, Real &tol) |
| Apply preconditioner to vector. | |
| virtual std::vector< std::vector< Real > > | checkGradient (const Vector< Real > &x, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1) |
| Finite-difference gradient check. | |
| virtual std::vector< std::vector< Real > > | checkGradient (const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &d, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1) |
| Finite-difference gradient check. | |
| virtual std::vector< std::vector< Real > > | checkGradient (const Vector< Real > &x, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1) |
| Finite-difference gradient check with specified step sizes. | |
| virtual std::vector< std::vector< Real > > | checkGradient (const Vector< Real > &x, const Vector< Real > &g, const Vector< Real > &d, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1) |
| Finite-difference gradient check with specified step sizes. | |
| virtual std::vector< std::vector< Real > > | checkHessVec (const Vector< Real > &x, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1) |
| Finite-difference Hessian-applied-to-vector check. | |
| virtual std::vector< std::vector< Real > > | checkHessVec (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const bool printToStream=true, std::ostream &outStream=std::cout, const int numSteps=ROL_NUM_CHECKDERIV_STEPS, const int order=1) |
| Finite-difference Hessian-applied-to-vector check. | |
| virtual std::vector< std::vector< Real > > | checkHessVec (const Vector< Real > &x, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1) |
| Finite-difference Hessian-applied-to-vector check with specified step sizes. | |
| virtual std::vector< std::vector< Real > > | checkHessVec (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const std::vector< Real > &steps, const bool printToStream=true, std::ostream &outStream=std::cout, const int order=1) |
| Finite-difference Hessian-applied-to-vector check with specified step sizes. | |
| virtual std::vector< Real > | checkHessSym (const Vector< Real > &x, const Vector< Real > &v, const Vector< Real > &w, const bool printToStream=true, std::ostream &outStream=std::cout) |
| Hessian symmetry check. | |
| virtual std::vector< Real > | checkHessSym (const Vector< Real > &x, const Vector< Real > &hv, const Vector< Real > &v, const Vector< Real > &w, const bool printToStream=true, std::ostream &outStream=std::cout) |
| Hessian symmetry check. | |
| virtual void | setParameter (const std::vector< Real > ¶m) |
Protected Member Functions | |
| const std::vector< Real > | getParameter (void) const |
Private Attributes | |
| Ptr< Vector< Real > > | prim_ |
| Ptr< Vector< Real > > | dual_ |
| Ptr< Vector< Real > > | basis_ |
| std::vector< Real > | param_ |
Detailed Description
class ROL::ROL::Objective< Real >
Provides the interface to evaluate objective functions.
Provides the definition of the objective function interface.
ROL's objective function interface is designed for Fr$eacute;chet differentiable functionals \(f:\mathcal{X}\to\mathbb{R}\), where \(\mathcal{X}\) is a Banach space. The basic operator interace, to be implemented by the user, requires:
- value – objective function evaluation.
It is strongly recommended that the user additionally overload:
- gradient – the objective function gradient – the default is a finite-difference approximation;
- hessVec – the action of the Hessian – the default is a finite-difference approximation.
The user may also overload:
- update – update the objective function at each new iteration;
- dirDeriv – compute the directional derivative – the default is a finite-difference approximation;
- invHessVec – the action of the inverse Hessian;
- precond – the action of a preconditioner for the Hessian.
Definition at line 78 of file ROL_Constraint_SerialSimOpt.hpp.
Constructor & Destructor Documentation
◆ ~Objective()
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inlinevirtual |
Definition at line 85 of file ROL_Constraint_SerialSimOpt.hpp.
◆ Objective()
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inline |
Definition at line 87 of file ROL_Constraint_SerialSimOpt.hpp.
Member Function Documentation
◆ update() [1/2]
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inlinevirtual |
Update objective function.
This function updates the objective function at new iterations.
- Parameters
-
[in] x is the new iterate. [in] type is the type of update requested. [in] iter is the outer algorithm iterations count.
Reimplemented in ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::AugmentedLagrangianObjective< Real >, and ROL::ROL::NonlinearLeastSquaresObjective< Real >.
Definition at line 96 of file ROL_Constraint_SerialSimOpt.hpp.
Referenced by ROL::ROL::TypeU::LineSearchAlgorithm< Real >::initialize(), and ROL::ROL::TypeU::LineSearchAlgorithm< Real >::run().
◆ update() [2/2]
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inlinevirtual |
Update objective function.
This function updates the objective function at new iterations.
- Parameters
-
[in] x is the new iterate. [in] flag is true if the iterate has changed. [in] iter is the outer algorithm iterations count.
Reimplemented in ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::NonlinearLeastSquaresObjective< Real >, and ROL::ROL::QuadraticPenalty< Real >.
Definition at line 109 of file ROL_Constraint_SerialSimOpt.hpp.
◆ value()
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pure virtual |
Compute value.
This function returns the objective function value.
- Parameters
-
[in] x is the current iterate. [in] tol is a tolerance for inexact objective function computation.
Implemented in ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::AugmentedLagrangianObjective< Real >, ROL::ROL::NonlinearLeastSquaresObjective< Real >, ROL::ROL::Objective_FSsolver< Real >, ROL::ROL::QuadraticPenalty< Real >, and ROL::ROL::TrustRegionModel_U< Real >.
Referenced by ROL::ROL::TypeU::LineSearchAlgorithm< Real >::initialize(), ROL::ROL::TypeU::LineSearchAlgorithm< Real >::run(), and ROL::FletcherStep< Real >::update().
◆ gradient()
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virtual |
Compute gradient.
This function returns the objective function gradient.
- Parameters
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[out] g is the gradient. [in] x is the current iterate. [in] tol is a tolerance for inexact objective function computation.
The default implementation is a finite-difference approximation based on the function value. This requires the definition of a basis \(\{\phi_i\}\) for the optimization vectors x and the definition of a basis \(\{\psi_j\}\) for the dual optimization vectors (gradient vectors g). The bases must be related through the Riesz map, i.e., \( R \{\phi_i\} = \{\psi_j\}\), and this must be reflected in the implementation of the ROL::Vector::dual() method.
Reimplemented in ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::AugmentedLagrangianObjective< Real >, ROL::ROL::NonlinearLeastSquaresObjective< Real >, ROL::ROL::Objective_FSsolver< Real >, ROL::ROL::QuadraticPenalty< Real >, and ROL::ROL::TrustRegionModel_U< Real >.
Definition at line 74 of file ROL_ObjectiveDef.hpp.
References ROL::ROL::Vector< Real >::axpy(), ROL::ROL::Vector< Real >::basis(), ROL::ROL::Vector< Real >::clone(), ROL::ROL::Vector< Real >::dimension(), ROL::ROL::Vector< Real >::dot(), ROL::Revert, ROL::ROL_EPSILON(), ROL::Temp, ROL::update(), value, ROL::ROL::Vector< Real >::zero(), and zero.
Referenced by ROL::FletcherBase< Real >::getGradient(), ROL::ROL::TypeU::LineSearchAlgorithm< Real >::initialize(), ROL::ROL::TypeU::LineSearchAlgorithm< Real >::run(), and ROL::FletcherStep< Real >::update().
◆ dirDeriv()
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virtual |
Compute directional derivative.
This function returns the directional derivative of the objective function in the \(d\) direction.
- Parameters
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[in] x is the current iterate. [in] d is the direction. [in] tol is a tolerance for inexact objective function computation.
Definition at line 54 of file ROL_ObjectiveDef.hpp.
References ROL::ROL::Vector< Real >::apply(), ROL::ROL::Vector< Real >::clone(), and ROL::ROL::Vector< Real >::dual().
◆ hessVec()
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virtual |
Apply Hessian approximation to vector.
This function applies the Hessian of the objective function to the vector \(v\).
- Parameters
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[out] hv is the the action of the Hessian on \(v\). [in] v is the direction vector. [in] x is the current iterate. [in] tol is a tolerance for inexact objective function computation.
Reimplemented in ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::AugmentedLagrangianObjective< Real >, ROL::ROL::NonlinearLeastSquaresObjective< Real >, ROL::ROL::Objective_FSsolver< Real >, ROL::ROL::QuadraticPenalty< Real >, and ROL::ROL::TrustRegionModel_U< Real >.
Definition at line 95 of file ROL_ObjectiveDef.hpp.
References ROL::ROL::Vector< Real >::axpy(), ROL::ROL::Vector< Real >::clone(), ROL::ROL::Vector< Real >::norm(), ROL::Revert, ROL::ROL::Vector< Real >::scale(), ROL::Temp, ROL::update(), ROL::ROL::Vector< Real >::zero(), and zero.
Referenced by ROL::ZOO::Objective_DiodeCircuit< Real >::hessVec(), and main().
◆ invHessVec()
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inlinevirtual |
Apply inverse Hessian approximation to vector.
This function applies the inverse Hessian of the objective function to the vector \(v\).
- Parameters
-
[out] hv is the action of the inverse Hessian on \(v\). [in] v is the direction vector. [in] x is the current iterate. [in] tol is a tolerance for inexact objective function computation.
Reimplemented in ROL::ROL::TrustRegionModel_U< Real >.
Definition at line 165 of file ROL_Constraint_SerialSimOpt.hpp.
◆ precond()
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inlinevirtual |
Apply preconditioner to vector.
This function applies a preconditioner for the Hessian of the objective function to the vector \(v\).
- Parameters
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[out] Pv is the action of the Hessian preconditioner on \(v\). [in] v is the direction vector. [in] x is the current iterate. [in] tol is a tolerance for inexact objective function computation.
Reimplemented in ROL::ROL::NonlinearLeastSquaresObjective< Real >, and ROL::ROL::TrustRegionModel_U< Real >.
Definition at line 183 of file ROL_Constraint_SerialSimOpt.hpp.
◆ checkGradient() [1/4]
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inlinevirtual |
Finite-difference gradient check.
This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output compares the error
\[ \left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|. \]
if the approximation is first order. More generally, difference approximation is
\[ \frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d) \]
where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps
- Parameters
-
[in] x is an optimization variable. [in] d is a direction vector. [in] printToStream is a flag that turns on/off output. [out] outStream is the output stream. [in] numSteps is a parameter which dictates the number of finite difference steps. [in] order is the order of the finite difference approximation (1,2,3,4)
Definition at line 209 of file ROL_Constraint_SerialSimOpt.hpp.
Referenced by main().
◆ checkGradient() [2/4]
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virtual |
Finite-difference gradient check.
This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output compares the error
\[ \left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|. \]
if the approximation is first order. More generally, difference approximation is
\[ \frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d) \]
where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps
- Parameters
-
[in] x is an optimization variable. [in] g is used to create a temporary gradient vector. [in] d is a direction vector. [in] printToStream is a flag that turns on/off output. [out] outStream is the output stream. [in] numSteps is a parameter which dictates the number of finite difference steps. [in] order is the order of the finite difference approximation (1,2,3,4)
Definition at line 119 of file ROL_ObjectiveDef.hpp.
◆ checkGradient() [3/4]
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inlinevirtual |
Finite-difference gradient check with specified step sizes.
This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output compares the error
\[ \left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|. \]
if the approximation is first order. More generally, difference approximation is
\[ \frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d) \]
where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps
- Parameters
-
[in] x is an optimization variable. [in] d is a direction vector. [in] steps is vector of steps of user-specified size. [in] printToStream is a flag that turns on/off output. [out] outStream is the output stream. [in] order is the order of the finite difference approximation (1,2,3,4)
Definition at line 269 of file ROL_Constraint_SerialSimOpt.hpp.
◆ checkGradient() [4/4]
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virtual |
Finite-difference gradient check with specified step sizes.
This function computes a sequence of one-sided finite-difference checks for the gradient.
At each step of the sequence, the finite difference step size is decreased. The output compares the error
\[ \left| \frac{f(x+td) - f(x)}{t} - \langle \nabla f(x),d\rangle_{\mathcal{X}^*,\mathcal{X}}\right|. \]
if the approximation is first order. More generally, difference approximation is
\[ \frac{1}{t} \sum\limits_{i=1}^m w_i f(x+t c_i d) \]
where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps
- Parameters
-
[in] x is an optimization variable. [in] g is used to create a temporary gradient vector. [in] d is a direction vector. [in] steps is vector of steps of user-specified size. [in] printToStream is a flag that turns on/off output. [out] outStream is the output stream. [in] order is the order of the finite difference approximation (1,2,3,4)
Definition at line 138 of file ROL_ObjectiveDef.hpp.
References ROL::ROL::Vector< Real >::apply(), ROL::ROL::Vector< Real >::clone(), ROL::ROL_EPSILON(), ROL::Finite_Difference_Arrays::shifts, ROL::Temp, ROL::update(), value, and ROL::Finite_Difference_Arrays::weights.
◆ checkHessVec() [1/4]
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inlinevirtual |
Finite-difference Hessian-applied-to-vector check.
This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output compares the error
\[ \left\| \frac{\nabla f(x+tv) - \nabla f(x)}{t} - \nabla^2 f(x)v\right\|_{\mathcal{X}^*}, \]
if the approximation is first order. More generally, difference approximation is
\[ \frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i v), \]
where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps
- Parameters
-
[in] x is an optimization variable. [in] v is a direction vector. [in] printToStream is a flag that turns on/off output. [out] outStream is the output stream. [in] numSteps is a parameter which dictates the number of finite difference steps. [in] order is the order of the finite difference approximation (1,2,3,4)
Definition at line 331 of file ROL_Constraint_SerialSimOpt.hpp.
Referenced by main().
◆ checkHessVec() [2/4]
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virtual |
Finite-difference Hessian-applied-to-vector check.
This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output compares the error
\[ \left\| \frac{\nabla f(x+tv) - \nabla f(x)}{t} - \nabla^2 f(x)v\right\|_{\mathcal{X}^*}, \]
if the approximation is first order. More generally, difference approximation is
\[ \frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i v), \]
where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps
- Parameters
-
[in] x is an optimization variable. [in] hv is used to create temporary gradient and Hessian-times-vector vectors. [in] v is a direction vector. [in] printToStream is a flag that turns on/off output. [out] outStream is the output stream. [in] numSteps is a parameter which dictates the number of finite difference steps. [in] order is the order of the finite difference approximation (1,2,3,4)
Definition at line 234 of file ROL_ObjectiveDef.hpp.
◆ checkHessVec() [3/4]
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inlinevirtual |
Finite-difference Hessian-applied-to-vector check with specified step sizes.
This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output compares the error
\[ \left\| \frac{\nabla f(x+tv) - \nabla f(x)}{t} - \nabla^2 f(x)v\right\|_{\mathcal{X}^*}, \]
if the approximation is first order. More generally, difference approximation is
\[ \frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i v), \]
where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps
- Parameters
-
[in] x is an optimization variable. [in] v is a direction vector. [in] steps is vector of steps of user-specified size. [in] printToStream is a flag that turns on/off output. [out] outStream is the output stream. [in] order is the order of the finite difference approximation (1,2,3,4)
Definition at line 392 of file ROL_Constraint_SerialSimOpt.hpp.
◆ checkHessVec() [4/4]
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virtual |
Finite-difference Hessian-applied-to-vector check with specified step sizes.
This function computes a sequence of one-sided finite-difference checks for the Hessian.
At each step of the sequence, the finite difference step size is decreased. The output compares the error
\[ \left\| \frac{\nabla f(x+tv) - \nabla f(x)}{t} - \nabla^2 f(x)v\right\|_{\mathcal{X}^*}, \]
if the approximation is first order. More generally, difference approximation is
\[ \frac{1}{t} \sum\limits_{i=1}^m w_i \nabla f(x+t c_i v), \]
where m = order+1, \(w_i\) are the difference weights and \(c_i\) are the difference steps
- Parameters
-
[in] x is an optimization variable. [in] hv is used to create temporary gradient and Hessian-times-vector vectors. [in] v is a direction vector. [in] steps is vector of steps of user-specified size. [in] printToStream is a flag that turns on/off output. [out] outStream is the output stream. [in] order is the order of the finite difference approximation (1,2,3,4)
Definition at line 253 of file ROL_ObjectiveDef.hpp.
References ROL::ROL::Vector< Real >::clone(), ROL::ROL_EPSILON(), ROL::Finite_Difference_Arrays::shifts, ROL::Temp, ROL::update(), and ROL::Finite_Difference_Arrays::weights.
◆ checkHessSym() [1/2]
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inlinevirtual |
Hessian symmetry check.
This function checks the symmetry of the Hessian by comparing
\[ \langle \nabla^2f(x)v,w\rangle_{\mathcal{X}^*,\mathcal{X}} \quad\text{and}\quad \langle \nabla^2f(x)w,v\rangle_{\mathcal{X}^*,\mathcal{X}}. \]
- Parameters
-
[in] x is an optimization variable. [in] v is a direction vector. [in] w is a direction vector. [in] printToStream is a flag that turns on/off output. [out] outStream is the output stream.
Definition at line 447 of file ROL_Constraint_SerialSimOpt.hpp.
Referenced by main().
◆ checkHessSym() [2/2]
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virtual |
Hessian symmetry check.
This function checks the symmetry of the Hessian by comparing
\[ \langle \nabla^2f(x)v,w\rangle_{\mathcal{X}^*,\mathcal{X}} \quad\text{and}\quad \langle \nabla^2f(x)w,v\rangle_{\mathcal{X}^*,\mathcal{X}}. \]
- Parameters
-
[in] x is an optimization variable. [in] hv is used to create temporary Hessian-times-vector vectors. [in] v is a direction vector. [in] w is a direction vector. [in] printToStream is a flag that turns on/off output. [out] outStream is the output stream.
Definition at line 350 of file ROL_ObjectiveDef.hpp.
References ROL::ROL::Vector< Real >::apply(), ROL::ROL::Vector< Real >::clone(), ROL::ROL_EPSILON(), ROL::Temp, and ROL::update().
◆ getParameter()
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inlineprotected |
Definition at line 484 of file ROL_Constraint_SerialSimOpt.hpp.
Referenced by DiffusionObjective< Real >::gradient_1(), DiffusionObjective< Real >::hessVec_11(), and DiffusionObjective< Real >::value().
◆ setParameter()
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inlinevirtual |
Reimplemented in ROL::AffineTransformObjective< Real >, ROL::CompositeObjective< Real >, ROL::CompositeObjective_SimOpt< Real >, ROL::LinearCombinationObjective< Real >, ROL::LinearCombinationObjective_SimOpt< Real >, ROL::MoreauYosidaPenalty< Real >, ROL::NonlinearLeastSquaresObjective< Real >, ROL::PH_bPOEObjective< Real >, ROL::PH_DeviationObjective< Real >, ROL::PH_ErrorObjective< Real >, ROL::PH_Objective< Real >, ROL::PH_ProbObjective< Real >, ROL::PH_RegretObjective< Real >, ROL::PH_RiskObjective< Real >, ROL::Reduced_AugmentedLagrangian_SimOpt< Real >, ROL::Reduced_Objective_SimOpt< Real >, ROL::RiskLessObjective< Real >, ROL::ROL::AffineTransformObjective< Real >, ROL::ROL::NonlinearLeastSquaresObjective< Real >, ROL::ScaledObjective< Real >, and ROL::SlacklessObjective< Real >.
Definition at line 489 of file ROL_Constraint_SerialSimOpt.hpp.
Referenced by ROL::CompositeObjective_SimOpt< Real >::setParameter(), ROL::LinearCombinationObjective_SimOpt< Real >::setParameter(), and ROL::Reduced_AugmentedLagrangian_SimOpt< Real >::setParameter().
Member Data Documentation
◆ prim_
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private |
Definition at line 81 of file ROL_Constraint_SerialSimOpt.hpp.
◆ dual_
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private |
Definition at line 81 of file ROL_Constraint_SerialSimOpt.hpp.
◆ basis_
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private |
Definition at line 81 of file ROL_Constraint_SerialSimOpt.hpp.
◆ param_
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private |
Definition at line 481 of file ROL_Constraint_SerialSimOpt.hpp.
The documentation for this class was generated from the following files:
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