SurrBasedLocalMinimizer Class Reference

and nonlinear least squares. More...

Inheritance diagram for SurrBasedLocalMinimizer:

List of all members.

Public Member Functions
	SurrBasedLocalMinimizer (Model &model)
	constructor
	~SurrBasedLocalMinimizer ()
	destructor
Private Member Functions
void	minimize_surrogates ()
	global, or hierarchical surrogates over a series of trust regions.
void	reset ()
	reset convergence controls in case of multiple SBLM executions
bool	tr_bounds (const RealVector &global_lower_bnds, const RealVector &global_upper_bnds, RealVector &tr_lower_bnds, RealVector &tr_upper_bnds)
	compute current trust region bounds
void	find_center_truth (const Iterator &dace_iterator, Model &truth_model)
	retrieve responseCenterTruth if possible, evaluate it if not
void	find_center_approx ()
	retrieve responseCenter_approx if possible, evaluate it if not
void	hard_convergence_check (const Response &response_truth, const RealVector &c_vars, const RealVector &lower_bnds, const RealVector &upper_bnds)
	merit function near zero)
void	tr_ratio_check (const RealVector &c_vars_star, const RealVector &tr_lower_bounds, const RealVector &tr_upper_bounds)
	region resizing) and check for soft convergence (diminishing returns)
void	update_penalty (const RealVector &fns_center_truth, const RealVector &fns_star_truth)
	initialize and update the penaltyParameter
void	relax_constraints (const RealVector &lower_bnds, const RealVector &upper_bnds)
	relax constraints by updating bounds when current iterate is infeasible
Static Private Member Functions
static void	approx_subprob_objective_eval (const Variables &surrogate_vars, const Variables &recast_vars, const Response &surrogate_response, Response &recast_response)
	static function used to define the approximate subproblem objective.
static void	approx_subprob_constraint_eval (const Variables &surrogate_vars, const Variables &recast_vars, const Response &surrogate_response, Response &recast_response)
	static function used to define the approximate subproblem constraints.
static void	hom_objective_eval (int &mode, int &n, double *tau_and_x, double &f, double *grad_f, int &)
	homotopy constraint relaxation formulation.
static void	hom_constraint_eval (int &mode, int &ncnln, int &n, int &nrowj, int *needc, double *tau_and_x, double *c, double *cjac, int &nstate)
	homotopy constraint relaxation formulation.
Private Attributes
Real	origTrustRegionFactor
	original user specification for trustRegionFactor
Real	trustRegionFactor
	bound - lower bound for each design variable).
Real	minTrustRegionFactor
	factor is reduced below the value of minTrustRegionFactor
Real	trRatioContractValue
	trust region ratio min value: contract tr if ratio below this value
Real	trRatioExpandValue
	trust region ratio sufficient value: expand tr if ratio above this value
Real	gammaContract
	trust region contraction factor
Real	gammaExpand
	trust region expansion factor
short	approxSubProbObj
	or AUGMENTED_LAGRANGIAN_OBJ
short	approxSubProbCon
	ORIGINAL_CON.
Model	approxSubProbModel
	involve a RecastModel recursion applied to iteratedModel
bool	recastSubProb
	flag to indicate when approxSubProbModel involves a RecastModel recursion
short	trConstraintRelax
	points: NO_RELAX or HOMOTOPY
short	meritFnType
	ADAPTIVE_PENALTY_MERIT, LAGRANGIAN_MERIT, or AUGMENTED_LAGRANGIAN_MERIT.
short	acceptLogic
	type of iterate acceptance test logic: FILTER or TR_RATIO
int	penaltyIterOffset
	for adaptive_penalty merit functions
short	convergenceFlag
	code indicating satisfaction of hard or soft convergence conditions
short	softConvCount
	count reaches softConvLimit, stop SBLM.
short	softConvLimit
	exceeded by softConvCount, stop SBLM.
bool	truthGradientFlag
	flags the use/availability of truth gradients within the SBLM process
bool	approxGradientFlag
	flags the use/availability of surrogate gradients within the SBLM process
bool	truthHessianFlag
	flags the use/availability of truth Hessians within the SBLM process
bool	approxHessianFlag
	flags the use/availability of surrogate Hessians within the SBLM process
bool	correctionFlag
	of each trust region
bool	globalApproxFlag
	flags the use of a global data fit surrogate (rsm, ann, mars, kriging)
bool	multiptApproxFlag
	flags the use of a multipoint data fit surrogate (TANA)
bool	localApproxFlag
	flags the use of a local data fit surrogate (Taylor series)
bool	hierarchApproxFlag
	flags the use of a model hierarchy/multifidelity surrogate
bool	newCenterFlag
	a new trust region center
bool	daceCenterPtFlag
	evaluations for global approximations (CCD, Box-Behnken)
bool	multiLayerBypassFlag
	(responseCenterTruth and responseStarTruth).
bool	useGradsFlag
	to be evaluated for each DACE point in global surrogate builds.
RealVector	nonlinIneqLowerBndsSlack
	individual violations of nonlinear inequality constraint lower bounds
RealVector	nonlinIneqUpperBndsSlack
	individual violations of nonlinear inequality constraint upper bounds
RealVector	nonlinEqTargetsSlack
	individual violations of nonlinear equality constraint targets
Real	tau
	constraint relaxation parameter
Real	alpha
	constraint relaxation parameter backoff parameter (multiplier)
Variables	varsCenter
	variables at the trust region center
Response	responseCenterApprox
	approx response at trust region center
Response	responseStarApprox
	approx response at SBLM cycle minimum
Response	responseCenterTruth
	truth response at trust region center
Response	responseStarTruth
	truth response at SBLM cycle minimum
Static Private Attributes
static SurrBasedLocalMinimizer *	sblmInstance
	pointer to SBLM instance used in static member functions

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Detailed Description

and nonlinear least squares.

This minimizer uses a SurrogateModel to perform minimization based on local, global, or hierarchical surrogates. It achieves provable convergence through the use of a sequence of trust regions and the application of surrogate corrections at the trust region centers.

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Member Function Documentation

void minimize_surrogates

(

)

[private, virtual]

global, or hierarchical surrogates over a series of trust regions.

Trust region-based strategy to perform surrogate-based optimization in subregions (trust regions) of the parameter space. The minimizer operates on approximations in lieu of the more expensive simulation-based response functions. The size of the trust region is varied according to the goodness of the agreement between the approximations and the true response functions.

Implements SurrBasedMinimizer.

void hard_convergence_check	(	const Response &	response_truth,
		const RealVector &	c_vars,
		const RealVector &	lower_bnds,
		const RealVector &	upper_bnds
	)			[private]

merit function near zero)

The hard convergence check computes the gradient of the merit function at the trust region center, performs a projection for active bound constraints (removing any gradient component directed into an active bound), and signals convergence if the 2-norm of this projected gradient is less than convergenceTol.

void tr_ratio_check	(	const RealVector &	c_vars_star,
		const RealVector &	tr_lower_bnds,
		const RealVector &	tr_upper_bnds
	)			[private]

region resizing) and check for soft convergence (diminishing returns)

Assess acceptance of SBLM iterate (trust region ratio or filter) and compute soft convergence metrics (number of consecutive failures, min trust region size, etc.) to assess whether the convergence rate has decreased to a point where the process should be terminated (diminishing returns).

void update_penalty	(	const RealVector &	fns_center_truth,
		const RealVector &	fns_star_truth
	)			[private]

initialize and update the penaltyParameter

Scaling of the penalty value is important to avoid rejecting SBLM iterates which must increase the objective to achieve a reduction in constraint violation. In the basic penalty case, the penalty is ramped exponentially based on the iteration counter. In the adaptive case, the ratio of relative change between center and star points for the objective and constraint violation values is used to rescale penalty values.

void approx_subprob_objective_eval	(	const Variables &	surrogate_vars,
		const Variables &	recast_vars,
		const Response &	surrogate_response,
		Response &	recast_response
	)			[static, private]

static function used to define the approximate subproblem objective.

Objective functions evaluator for solution of approximate subproblem using a RecastModel.

void approx_subprob_constraint_eval	(	const Variables &	surrogate_vars,
		const Variables &	recast_vars,
		const Response &	surrogate_response,
		Response &	recast_response
	)			[static, private]

static function used to define the approximate subproblem constraints.

Constraint functions evaluator for solution of approximate subproblem using a RecastModel.

void hom_objective_eval	(	int &	mode,
		int &	n,
		double *	tau_and_x,
		double &	f,
		double *	grad_f,
		int &
	)			[static, private]

homotopy constraint relaxation formulation.

NPSOL objective functions evaluator for solution of homotopy constraint relaxation parameter optimization. This constrained optimization problem performs the update of the tau parameter in the homotopy heuristic approach used to relax the constraints in the original problem .

void hom_constraint_eval	(	int &	mode,
		int &	ncnln,
		int &	n,
		int &	nrowj,
		int *	needc,
		double *	tau_and_x,
		double *	c,
		double *	cjac,
		int &	nstate
	)			[static, private]

homotopy constraint relaxation formulation.

NPSOL constraint functions evaluator for solution of homotopy constraint relaxation parameter optimization. This constrained optimization problem performs the update of the tau parameter in the homotopy heuristic approach used to relax the constraints in the original problem.

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

• SurrBasedLocalMinimizer.H
• SurrBasedLocalMinimizer.C

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