RVLUmin::TRGNStep< Scalar, Policy > Class Template Reference

Generic trust region (truncated GN) step. More...

#include <TRGNAlg.hh>

Inheritance diagram for RVLUmin::TRGNStep< Scalar, Policy >:

List of all members.

Public Member Functions
void	run ()
	here op = b-F(x), i.e.
atype	getDelta ()
	TRGNStep (Policy const &_pol, OperatorEvaluation< Scalar > &_opeval, atype _eta1, atype _eta2, atype _gamma1, atype _gamma2, atype _minstep, bool &_nostep, atype &_predred, atype &_actred, atype &_jval, atype &_agnrm, atype &_rgnrm, ostream &_str)
	constructor
	~TRGNStep ()

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Detailed Description

template<typename Scalar, typename Policy>
class RVLUmin::TRGNStep< Scalar, Policy >

Generic trust region (truncated GN) step.

Trust region decision parameters are constants, so pass by value.

Operator evaluation, Function value, absolute and relative gradient norms, predicted and actual reduction, and trust radius are all altered by this object, so it stores mutable references for these items.

Parameters / data members:

• pol - solver policy, see description in TRGNAlg docs (TRGNAlg is a policy subclass). Generates LS solver via build method. On construction, an LS solver is required to initialize the residual norm and normal residual norm, passed by reference, as well as the RVL::Vector update.
• opeval - RVL::OperatorEvaluation, mutable reference, 0.5*getValue().normsq() = objective function
• eta1 - lower G-A parameter; when actred/predred < eta1, trust radius reduced. Typical value = 0.01
• eta2 - upper G-A parameter; when actred/predred > eta2 and trust region constraint is binding, trust radius increased. Typical value = 0.9
• gamma1 - trust region reduction factor. Typical value = 0.5
• gamma2 - trust region increase factor. Typical value = 1.8
• predred - predicted reduction - mutable reference
• actred - actual reduction - mutable reference
• jval - objective function value - mutable reference
• agnrm - gradient norm - mutable reference
• rgnrm - gradient norm scaled by reciprocal of initial (on constr) - mutable reference
• Delta - trust radius - mutable reference
• str - verbose output stream

Outline of run() method:

• call trust region least squares solver to return step
• create trial iterate (storing input iterate in case of rejection)
• compute predicted, actual reductions in objective (predred, actred)
• if actred/predred < eta1, reduce trust radius by factor gamma1, reject step, restore iterate from stored input
• if actred/predred >= eta1, accept step (discard stored input)
  • if additionally actred/predred > eta2 and trust region constraint was binding on LS solution, increase trust radius by factor gamma2
• return

Definition at line 57 of file TRGNAlg.hh.

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Constructor & Destructor Documentation

template<typename Scalar, typename Policy>

RVLUmin::TRGNStep< Scalar, Policy >::TRGNStep	(	Policy const &	_pol,
		OperatorEvaluation< Scalar > &	_opeval,
		atype	_eta1,
		atype	_eta2,
		atype	_gamma1,
		atype	_gamma2,
		atype	_minstep,
		bool &	_nostep,
		atype &	_predred,
		atype &	_actred,
		atype &	_jval,
		atype &	_agnrm,
		atype &	_rgnrm,
		ostream &	_str
	)

constructor

Depends on least-squares solver, chosen by the policy argument. Type of this object passed as template parameter. For characteristics, see TRGNAlg docs.

Pass already-initialized operator evaluation to this method. This evaluation stores the RHS (opeval.getValue()) and LinearOp (opeval.getDeriv) of the G-N least squares problem. The evaluation point is updated as part of the step, so the opeval reference must be mutable.

Parameters:

	_pol	- solver policy, see descriptions in TRGNAlg docs
	_opeval	- updated reference, 0.5*getValue().normsq() = objective function
	_eta1	lower G-A parameter > 0
	_eta2	upper G-A parameter > eta1
	_gamma1	trust region reduction factor < 1
	_gamma2	trust region expansion factor > 1, gamma1*gamma2 < 1
	_minstep	min permitted step as a fraction of trust radius
	_nostep	true if step norm was too small rel trust radius
	_predred	predicted reduction - updated reference
	_actred	actual reduction - updated reference
	_jval	objective function value - updated reference
	_agnrm	gradient norm - updated reference
	_rgnrm	gradient norm scaled by reciprocal of original (on constr) - updated reference
	_str	verbose output stream

Requirements on parameters:

• Delta >= 0
• 0 < gamma1 < 1 < gamma2
• gamma1 * gamma2 < 1
• 0 < eta1 < eta2
• opeval = operator defining nonlinear least squares problem, evaluated at current iterate. used to supply RHS (getValue) and LinearOp (getDeriv) of G-N problem on call, and to evaluate residual and normal residual at G-N solution on return.
• pol - TRLS solver policy, as described above

Definition at line 234 of file TRGNAlg.hh.

template<typename Scalar, typename Policy>

RVLUmin::TRGNStep< Scalar, Policy >::~TRGNStep

(

)

Definition at line 305 of file TRGNAlg.hh.

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Member Function Documentation

template<typename Scalar, typename Policy>

void RVLUmin::TRGNStep< Scalar, Policy >::run

(

)

[virtual]

here op = b-F(x), i.e.

the residual - use ResidualOp wrapper

NOTE: this is the "optimistic" no-copy form - i.e. assumes that the step is likely to succeed, so the restor-xsave-compute branch is unlikely, hence not costly. A "pessimistic" form would be a mirror-image. The optimal form would involve a deep copy operation on OpEvals, which is certainly possible future mod.

the quadratic model is

0.5*\|b-F(x)\|^2 + p^Tg(x) + 0.5p^TH(x)p

where H(x)=DF(x)^TDF(x), and H(x)p = g(x) = DF(x)^T(b-F(x)) (approx)

The predicted reduction is

0.5*\|b-F(x)\|^2 - 0.5p^Tg(x)

Implements RVLAlg::Algorithm.

Definition at line 82 of file TRGNAlg.hh.

References RVL::Vector< Scalar >::copy(), RVL::Vector< Scalar >::linComb(), RVLAlg::Terminator::query(), and RVLAlg::Algorithm::run().

template<typename Scalar, typename Policy>

atype RVLUmin::TRGNStep< Scalar, Policy >::getDelta

(

)

Definition at line 194 of file TRGNAlg.hh.

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

• TRGNAlg.hh

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