Class for provably-convergent local surrogate-based optimization and nonlinear least squares. More...

Inheritance diagram for SurrBasedLocalMinimizer:

Public Member Functions
	SurrBasedLocalMinimizer (ProblemDescDB &problem_db, Model &model, std::shared_ptr< TraitsBase > traits)
	constructor

	~SurrBasedLocalMinimizer ()
	destructor

Protected Member Functions
void	initialize_graphics (int iterator_server_id=1)
	initialize graphics customized for surrogate-based iteration More...

void	pre_run ()
	pre-run portion of run (optional); re-implemented by Iterators which can generate all Variables (parameter sets) a priori More...

void	core_run ()
	Performs local surrogate-based minimization by minimizing local, global, or hierarchical surrogates over a series of trust regions. More...

void	post_run (std::ostream &s)
	post-run portion of run (optional); verbose to print results; re-implemented by Iterators that can read all Variables/Responses and perform final analysis phase in a standalone way More...

void	reset ()
	restore initial state for repeated sub-iterator executions

virtual SurrBasedLevelData &	trust_region ()=0
	return the active SurrBasedLevelData instance

virtual void	update_trust_region ()=0
	update the trust region bounds, strictly contained within global bounds

virtual void	build ()=0
	build the approximation over the current trust region

virtual void	minimize ()
	solve the approximate subproblem

virtual void	verify ()=0
	verify the approximate iterate and update the trust region for the next approximate optimization cycle

virtual unsigned short	converged ()=0
	return the convergence code for the truth level of the trust region hierarchy

void	initialize_sub_model ()
	construct and initialize approxSubProbModel

void	initialize_sub_minimizer ()
	construct and initialize approxSubProbMinimizer

void	initialize_multipliers ()
	initialize lagrangeMult and augLagrangeMult

void	reset_penalties ()
	reset all penalty parameters to their initial values

void	reset_multipliers ()
	reset Lagrange multipliers to initial values for cases where they are accumulated instead of computed directly

void	update_trust_region_data (SurrBasedLevelData &tr_data, const RealVector &parent_l_bnds, const RealVector &parent_u_bnds)
	update the trust region bounds, strictly contained within global bounds

void	update_approx_sub_problem (SurrBasedLevelData &tr_data)
	update variables and bounds within approxSubProbModel

void	compute_trust_region_ratio (SurrBasedLevelData &tr_data, bool check_interior=false)
	compute trust region ratio (for SBLM iterate acceptance and trust region resizing) and check for soft convergence (diminishing returns) More...

void	hard_convergence_check (SurrBasedLevelData &tr_data, const RealVector &lower_bnds, const RealVector &upper_bnds)
	check for hard convergence (norm of projected gradient of merit function < tolerance) More...

void	print_convergence_code (std::ostream &s, unsigned short code)
	print out the state corresponding to the code returned by converged()

void	update_penalty (const RealVector &fns_center_truth, const RealVector &fns_star_truth)
	initialize and update the penaltyParameter More...

bool	find_approx_response (const Variables &search_vars, Response &search_resp)
	locate an approximate response with the data_pairs cache

bool	find_truth_response (const Variables &search_vars, Response &search_resp)
	locate a truth response with the data_pairs cache

bool	find_response (const Variables &search_vars, Response &search_resp, const String &search_id, short set_request)
	locate a response with the data_pairs cache

void	relax_constraints (SurrBasedLevelData &tr_data)
	relax constraints by updating bounds when current iterate is infeasible

Protected Member Functions inherited from SurrBasedMinimizer
	SurrBasedMinimizer (ProblemDescDB &problem_db, Model &model, std::shared_ptr< TraitsBase > traits)
	constructor

	~SurrBasedMinimizer ()
	destructor

void	derived_init_communicators (ParLevLIter pl_iter)
	derived class contributions to initializing the communicators associated with this Iterator instance

void	derived_set_communicators (ParLevLIter pl_iter)
	derived class contributions to setting the communicators associated with this Iterator instance

void	derived_free_communicators (ParLevLIter pl_iter)
	derived class contributions to freeing the communicators associated with this Iterator instance

void	print_results (std::ostream &s, short results_state=FINAL_RESULTS)

void	update_lagrange_multipliers (const RealVector &fn_vals, const RealMatrix &fn_grads, SurrBasedLevelData &tr_data)
	initialize and update Lagrange multipliers for basic Lagrangian More...

void	update_augmented_lagrange_multipliers (const RealVector &fn_vals)
	initialize and update the Lagrange multipliers for augmented Lagrangian More...

void	initialize_filter (SurrBasedLevelData &tr_data, const RealVector &fn_vals)
	(re-)initialize filter from a set of function values

bool	update_filter (SurrBasedLevelData &tr_data, const RealVector &fn_vals)
	update filter using a new set of function values More...

Real	lagrangian_merit (const RealVector &fn_vals, const BoolDeque &sense, const RealVector &primary_wts, const RealVector &nln_ineq_l_bnds, const RealVector &nln_ineq_u_bnds, const RealVector &nln_eq_tgts)
	compute a Lagrangian function from a set of function values More...

void	lagrangian_gradient (const RealVector &fn_vals, const RealMatrix &fn_grads, const BoolDeque &sense, const RealVector &primary_wts, const RealVector &nln_ineq_l_bnds, const RealVector &nln_ineq_u_bnds, const RealVector &nln_eq_tgts, RealVector &lag_grad)
	compute the gradient of the Lagrangian function

void	lagrangian_hessian (const RealVector &fn_vals, const RealMatrix &fn_grads, const RealSymMatrixArray &fn_hessians, const BoolDeque &sense, const RealVector &primary_wts, const RealVector &nln_ineq_l_bnds, const RealVector &nln_ineq_u_bnds, const RealVector &nln_eq_tgts, RealSymMatrix &lag_hess)
	compute the Hessian of the Lagrangian function

Real	augmented_lagrangian_merit (const RealVector &fn_vals, const BoolDeque &sense, const RealVector &primary_wts, const RealVector &nln_ineq_l_bnds, const RealVector &nln_ineq_u_bnds, const RealVector &nln_eq_tgts)
	compute an augmented Lagrangian function from a set of function values More...

void	augmented_lagrangian_gradient (const RealVector &fn_vals, const RealMatrix &fn_grads, const BoolDeque &sense, const RealVector &primary_wts, const RealVector &nln_ineq_l_bnds, const RealVector &nln_ineq_u_bnds, const RealVector &nln_eq_tgts, RealVector &alag_grad)
	compute the gradient of the augmented Lagrangian function

void	augmented_lagrangian_hessian (const RealVector &fn_vals, const RealMatrix &fn_grads, const RealSymMatrixArray &fn_hessians, const BoolDeque &sense, const RealVector &primary_wts, const RealVector &nln_ineq_l_bnds, const RealVector &nln_ineq_u_bnds, const RealVector &nln_eq_tgts, RealSymMatrix &alag_hess)
	compute the Hessian of the augmented Lagrangian function

Real	penalty_merit (const RealVector &fn_vals, const BoolDeque &sense, const RealVector &primary_wts)
	compute a penalty function from a set of function values More...

void	penalty_gradient (const RealVector &fn_vals, const RealMatrix &fn_grads, const BoolDeque &sense, const RealVector &primary_wts, RealVector &pen_grad)
	compute the gradient of the penalty function

Real	constraint_violation (const RealVector &fn_vals, const Real &constraint_tol)
	compute the constraint violation from a set of function values More...

Protected Member Functions inherited from Minimizer
	Minimizer (std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
	default constructor

	Minimizer (ProblemDescDB &problem_db, Model &model, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
	standard constructor More...

	Minimizer (unsigned short method_name, Model &model, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
	alternate constructor for "on the fly" instantiations

	Minimizer (unsigned short method_name, size_t num_lin_ineq, size_t num_lin_eq, size_t num_nln_ineq, size_t num_nln_eq, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
	alternate constructor for "on the fly" instantiations

	~Minimizer ()
	destructor

void	update_from_model (const Model &model)
	set inherited data attributes based on extractions from incoming model

void	initialize_run ()
	utility function to perform common operations prior to pre_run(); typically memory initialization; setting of instance pointers More...

void	finalize_run ()
	utility function to perform common operations following post_run(); deallocation and resetting of instance pointers More...

const Model &	algorithm_space_model () const

Model	original_model (unsigned short recasts_left=0) const
	Return a shallow copy of the original model this Iterator was originally passed, optionally leaving recasts_left on top of it.

void	data_transform_model ()
	Wrap iteratedModel in a RecastModel that subtracts provided observed data from the primary response functions (variables and secondary responses are unchanged) More...

void	scale_model ()
	Wrap iteratedModel in a RecastModel that performs variable and/or response scaling. More...

Real	objective (const RealVector &fn_vals, const BoolDeque &max_sense, const RealVector &primary_wts) const
	compute a composite objective value from one or more primary functions More...

Real	objective (const RealVector &fn_vals, size_t num_fns, const BoolDeque &max_sense, const RealVector &primary_wts) const
	compute a composite objective with specified number of source primary functions, instead of userPrimaryFns More...

void	objective_gradient (const RealVector &fn_vals, const RealMatrix &fn_grads, const BoolDeque &max_sense, const RealVector &primary_wts, RealVector &obj_grad) const
	compute the gradient of the composite objective function

void	objective_gradient (const RealVector &fn_vals, size_t num_fns, const RealMatrix &fn_grads, const BoolDeque &max_sense, const RealVector &primary_wts, RealVector &obj_grad) const
	compute the gradient of the composite objective function More...

void	objective_hessian (const RealVector &fn_vals, const RealMatrix &fn_grads, const RealSymMatrixArray &fn_hessians, const BoolDeque &max_sense, const RealVector &primary_wts, RealSymMatrix &obj_hess) const
	compute the Hessian of the composite objective function

void	objective_hessian (const RealVector &fn_vals, size_t num_fns, const RealMatrix &fn_grads, const RealSymMatrixArray &fn_hessians, const BoolDeque &max_sense, const RealVector &primary_wts, RealSymMatrix &obj_hess) const
	compute the Hessian of the composite objective function More...

virtual void	archive_best_results ()
	top-level archival method

void	archive_best_variables (const bool active_only=false) const
	archive best variables for the index'th final solution

void	archive_best_objective_functions () const
	archive the index'th set of objective functions

void	archive_best_constraints () const
	archive the index'th set of constraints

void	archive_best_residuals () const
	Archive residuals when calibration terms are used.

void	resize_best_vars_array (size_t newsize)
	Safely resize the best variables array to newsize taking into account the envelope-letter design pattern and any recasting. More...

void	resize_best_resp_array (size_t newsize)
	Safely resize the best response array to newsize taking into account the envelope-letter design pattern and any recasting. More...

void	local_recast_retrieve (const Variables &vars, Response &response) const
	infers MOO/NLS solution from the solution of a single-objective optimizer More...

Protected Member Functions inherited from Iterator
	Iterator (BaseConstructor, ProblemDescDB &problem_db, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
	constructor initializes the base class part of letter classes (BaseConstructor overloading avoids infinite recursion in the derived class constructors - Coplien, p. 139) More...

	Iterator (NoDBBaseConstructor, unsigned short method_name, Model &model, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
	alternate constructor for base iterator classes constructed on the fly More...

	Iterator (NoDBBaseConstructor, unsigned short method_name, std::shared_ptr< TraitsBase > traits=std::shared_ptr< TraitsBase >(new TraitsBase()))
	alternate constructor for base iterator classes constructed on the fly More...

virtual const VariablesArray &	initial_points () const
	gets the multiple initial points for this iterator. This will only be meaningful after a call to initial_points mutator.

StrStrSizet	run_identifier () const
	get the unique run identifier based on method name, id, and number of executions

void	initialize_model_graphics (Model &model, int iterator_server_id)
	helper function that encapsulates initialization operations, modular on incoming Model instance More...

void	export_final_surrogates (Model &data_fit_surr_model)
	export final surrogates generated, e.g., GP in EGO and friends More...

Static Protected 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. More...

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. More...

static void	hom_objective_eval (int &mode, int &n, double tau_and_x, double &f, double grad_f, int &)
	static function used by NPSOL as the objective function in the homotopy constraint relaxation formulation. More...

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)
	static function used by NPSOL as the constraint function in the homotopy constraint relaxation formulation. More...

Protected Attributes
Model	approxSubProbModel
	the approximate sub-problem formulation solved on each approximate minimization cycle: may be a shallow copy of iteratedModel, or may involve a RecastModel recursion applied to iteratedModel

short	approxSubProbObj
	type of approximate subproblem objective: ORIGINAL_OBJ, LAGRANGIAN_OBJ, or AUGMENTED_LAGRANGIAN_OBJ

short	approxSubProbCon
	type of approximate subproblem constraints: NO_CON, LINEARIZED_CON, or ORIGINAL_CON

bool	recastSubProb
	flag to indicate when approxSubProbModel involves a RecastModel recursion

short	meritFnType
	type of merit function used in trust region ratio logic: PENALTY_MERIT, ADAPTIVE_PENALTY_MERIT, LAGRANGIAN_MERIT, or AUGMENTED_LAGRANGIAN_MERIT

short	acceptLogic
	type of iterate acceptance test logic: FILTER or TR_RATIO

short	trConstraintRelax
	type of trust region constraint relaxation for infeasible starting points: NO_RELAX or HOMOTOPY

int	minimizeCycles
	counter for number of minimization cycles that have accumulated prior to convergence at the minimizeIndex level (used for ramping penalties)

int	penaltyIterOffset
	iteration offset used to update the scaling of the penalty parameter for adaptive_penalty merit functions

RealVector	origTrustRegionFactor
	original user specification for trust region initial_size

Real	minTrustRegionFactor
	a soft convergence control: stop SBLM when the trust region 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

unsigned short	softConvLimit
	convergence control limiting the number of consecutive iterations that fail to achieve sufficient decrease. If exceeded by softConvCount, stop.

short	truthSetRequest
	derivative order of truth data used within the SBLM process

short	approxSetRequest
	derivative order of surrogate data used within the SBLM process

short	correctionType
	flags the use of surrogate correction techniques at the center of each trust region

RealVector	initialPoint
	starting point prior to sequence of SBLM iterations

RealVector	globalLowerBnds
	Global lower bounds.

RealVector	globalUpperBnds
	Global Upper bounds.

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)

Protected Attributes inherited from SurrBasedMinimizer
Iterator	approxSubProbMinimizer
	the minimizer used on the surrogate model to solve the approximate subproblem on each surrogate-based iteration

size_t	globalIterCount
	global iteration counter corresponding to number of surrogate-based minimizations

RealVector	lagrangeMult
	Lagrange multipliers for basic Lagrangian calculations.

RealVector	augLagrangeMult
	Lagrange multipliers for augmented Lagrangian calculations.

Real	penaltyParameter
	the penalization factor for violated constraints used in quadratic penalty calculations; increased in update_penalty()

RealVector	origNonlinIneqLowerBnds
	original nonlinear inequality constraint lower bounds (no relaxation)

RealVector	origNonlinIneqUpperBnds
	original nonlinear inequality constraint upper bounds (no relaxation)

RealVector	origNonlinEqTargets
	original nonlinear equality constraint targets (no relaxation)

Real	eta
	constant used in etaSequence updates

Real	alphaEta
	power for etaSequence updates when updating penalty

Real	betaEta
	power for etaSequence updates when updating multipliers

Real	etaSequence
	decreasing sequence of allowable constraint violation used in augmented Lagrangian updates (refer to Conn, Gould, and Toint, section 14.4)

size_t	miPLIndex
	index for the active ParallelLevel within ParallelConfiguration::miPLIters

Protected Attributes inherited from Minimizer
size_t	numFunctions
	number of response functions

size_t	numContinuousVars
	number of active continuous vars

size_t	numDiscreteIntVars
	number of active discrete integer vars

size_t	numDiscreteStringVars
	number of active discrete string vars

size_t	numDiscreteRealVars
	number of active discrete real vars

Real	constraintTol
	optimizer/least squares constraint tolerance

Real	bigRealBoundSize
	cutoff value for inequality constraint and continuous variable bounds

int	bigIntBoundSize
	cutoff value for discrete variable bounds

size_t	numNonlinearIneqConstraints
	number of nonlinear inequality constraints

size_t	numNonlinearEqConstraints
	number of nonlinear equality constraints

size_t	numLinearIneqConstraints
	number of linear inequality constraints

size_t	numLinearEqConstraints
	number of linear equality constraints

size_t	numNonlinearConstraints
	total number of nonlinear constraints

size_t	numLinearConstraints
	total number of linear constraints

size_t	numConstraints
	total number of linear and nonlinear constraints

bool	optimizationFlag
	flag for use where optimization and NLS must be distinguished

size_t	numUserPrimaryFns
	number of objective functions or least squares terms in the inbound model; always initialize at Minimizer, even if overridden later

size_t	numIterPrimaryFns
	number of objective functions or least squares terms in iterator's view, after transformations; always initialize at Minimizer, even if overridden later

bool	boundConstraintFlag
	convenience flag for denoting the presence of user-specified bound constraints. Used for method selection and error checking.

bool	speculativeFlag
	flag for speculative gradient evaluations

bool	calibrationDataFlag
	flag indicating whether user-supplied calibration data is active

ExperimentData	expData
	Container for experimental data to which to calibrate model using least squares or other formulations which minimize SSE.

size_t	numExperiments
	number of experiments

size_t	numTotalCalibTerms
	number of total calibration terms (sum over experiments of number of experimental data per experiment, including field data)

Model	dataTransformModel
	Shallow copy of the data transformation model, when present (cached in case further wrapped by other transformations)

bool	scaleFlag
	whether Iterator-level scaling is active

Model	scalingModel
	Shallow copy of the scaling transformation model, when present (cached in case further wrapped by other transformations)

Minimizer *	prevMinInstance
	pointer containing previous value of minimizerInstance

bool	vendorNumericalGradFlag
	convenience flag for gradient_type == numerical && method_source == vendor

std::shared_ptr< TPLDataTransfer >	dataTransferHandler
	Emerging helper class for handling data transfers to/from Dakota and the underlying TPL.

Protected Attributes inherited from Iterator
ProblemDescDB &	probDescDB
	class member reference to the problem description database More...

ParallelLibrary &	parallelLib
	class member reference to the parallel library

ParConfigLIter	methodPCIter
	the active ParallelConfiguration used by this Iterator instance

Model	iteratedModel
	the model to be iterated (for iterators and meta-iterators employing a single model instance)

size_t	myModelLayers
	number of Models locally (in Iterator or derived classes) wrapped around the initially passed in Model

unsigned short	methodName
	name of the iterator (the user's method spec)

Real	convergenceTol
	iteration convergence tolerance

size_t	maxIterations
	maximum number of iterations for the method

size_t	maxFunctionEvals
	maximum number of fn evaluations for the method

int	maxEvalConcurrency
	maximum number of concurrent model evaluations More...

ActiveSet	activeSet
	the response data requirements on each function evaluation

size_t	numFinalSolutions
	number of solutions to retain in best variables/response arrays

VariablesArray	bestVariablesArray
	collection of N best solution variables found during the study; always in context of Model originally passed to the Iterator (any in-flight Recasts must be undone)

ResponseArray	bestResponseArray
	collection of N best solution responses found during the study; always in context of Model originally passed to the Iterator (any in-flight Recasts must be undone)

bool	subIteratorFlag
	flag indicating if this Iterator is a sub-iterator (NestedModel::subIterator or DataFitSurrModel::daceIterator)

short	outputLevel
	output verbosity level: {SILENT,QUIET,NORMAL,VERBOSE,DEBUG}_OUTPUT

bool	summaryOutputFlag
	flag for summary output (evaluation stats, final results); default true, but false for on-the-fly (helper) iterators and sub-iterator use cases

ResultsManager &	resultsDB
	reference to the global iterator results database

EvaluationStore &	evaluationsDB
	reference to the global evaluation database

EvaluationsDBState	evaluationsDBState
	State of evaluations DB for this iterator.

ResultsNames	resultsNames
	valid names for iterator results

std::shared_ptr< TraitsBase >	methodTraits
	pointer that retains shared ownership of a TraitsBase object, or child thereof

bool	topLevel
	Whether this is the top level iterator.

bool	exportSurrogate = false
	whether to export final surrogates

String	surrExportPrefix
	base filename for exported surrogates

unsigned short	surrExportFormat = NO_MODEL_FORMAT
	(bitwise) format(s) to export

Static Protected Attributes
static SurrBasedLocalMinimizer *	sblmInstance
	pointer to SBLM instance used in static member functions

Additional Inherited Members
Static Public Member Functions inherited from Minimizer
static Real	sum_squared_residuals (size_t num_pri_fns, const RealVector &residuals, const RealVector &weights)
	return weighted sum of squared residuals

static void	print_residuals (size_t num_terms, const RealVector &best_terms, const RealVector &weights, size_t num_best, size_t best_index, std::ostream &s)
	print num_terms residuals and misfit for final results

static void	print_model_resp (size_t num_pri_fns, const RealVector &best_fns, size_t num_best, size_t best_index, std::ostream &s)
	print the original user model resp in the case of data transformations

Detailed Description

Class for provably-convergent local surrogate-based optimization 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.

Member Function Documentation

void initialize_graphics ( int iterator_server_id = 1)

protectedvirtual

initialize graphics customized for surrogate-based iteration

Surrogate-based local (data-fit) specializes graphics to output trust region centers. See OutputManager::add_tabular_data in DataFitSurrBasedLocalMinimizer. Other children don't do any output

Reimplemented from Iterator.

References Model::create_2d_plots(), Model::create_tabular_datastream(), OutputManager::graph2DFlag, OutputManager::graphics(), OutputManager::graphics_counter(), Iterator::iteratedModel, Iterator::methodName, ParallelLibrary::output_manager(), Iterator::parallelLib, Graphics::set_x_labels2d(), OutputManager::tabular_counter_label(), OutputManager::tabularDataFlag, and Model::truth_model().

void pre_run ( )

protectedvirtual

pre-run portion of run (optional); re-implemented by Iterators which can generate all Variables (parameter sets) a priori

pre-run phase, which a derived iterator may optionally reimplement; when not present, pre-run is likely integrated into the derived run function. This is a virtual function; when re-implementing, a derived class must call its nearest parent's pre_run(), if implemented, typically before performing its own implementation steps.

Reimplemented from Iterator.

References Model::continuous_lower_bounds(), Model::continuous_upper_bounds(), Model::continuous_variables(), SurrBasedLocalMinimizer::converged(), Dakota::copy_data(), SurrBasedLocalMinimizer::globalLowerBnds, SurrBasedLocalMinimizer::globalUpperBnds, SurrBasedLocalMinimizer::initialPoint, Iterator::iteratedModel, and SurrBasedLocalMinimizer::reset().

void core_run ( )

protectedvirtual

Performs local surrogate-based minimization by minimizing local, 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 adapted according to the agreement between the approximations and the true response functions.

Reimplemented from Iterator.

References SurrBasedLocalMinimizer::build(), SurrBasedLocalMinimizer::converged(), SurrBasedLocalMinimizer::minimize(), SurrBasedLocalMinimizer::sblmInstance, SurrBasedLocalMinimizer::update_trust_region(), and SurrBasedLocalMinimizer::verify().

void post_run ( std::ostream & s)

protectedvirtual

post-run portion of run (optional); verbose to print results; re-implemented by Iterators that can read all Variables/Responses and perform final analysis phase in a standalone way

Post-run phase, which a derived iterator may optionally reimplement; when not present, post-run is likely integrated into run. This is a virtual function; when re-implementing, a derived class must call its nearest parent's post_run(), typically after performing its own implementation steps.

Reimplemented from Minimizer.

References SurrBasedLocalMinimizer::converged(), SurrBasedMinimizer::globalIterCount, Minimizer::post_run(), and SurrBasedLocalMinimizer::print_convergence_code().

void compute_trust_region_ratio	(	SurrBasedLevelData &	tr_data,
		bool	check_interior = `false`
	)

protected

compute trust region ratio (for SBLM iterate acceptance and trust 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 hard_convergence_check	(	SurrBasedLevelData &	tr_data,
		const RealVector &	lower_bnds,
		const RealVector &	upper_bnds
	)

protected

check for hard convergence (norm of projected gradient of merit function < tolerance)

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.

References SurrBasedLocalMinimizer::approxSubProbObj, SurrBasedMinimizer::constraint_violation(), Minimizer::constraintTol, Iterator::convergenceTol, Response::function_gradients(), Response::function_values(), Iterator::iteratedModel, SurrBasedMinimizer::lagrangian_gradient(), SurrBasedLocalMinimizer::meritFnType, SurrBasedLocalMinimizer::minimizeCycles, Minimizer::numContinuousVars, Minimizer::numNonlinearConstraints, SurrBasedMinimizer::origNonlinEqTargets, SurrBasedMinimizer::origNonlinIneqLowerBnds, SurrBasedMinimizer::origNonlinIneqUpperBnds, Iterator::outputLevel, Model::primary_response_fn_sense(), Model::primary_response_fn_weights(), SurrBasedLocalMinimizer::truthSetRequest, SurrBasedMinimizer::update_augmented_lagrange_multipliers(), and SurrBasedMinimizer::update_lagrange_multipliers().

void update_penalty	(	const RealVector &	fns_center_truth,
		const RealVector &	fns_star_truth
	)

protected

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.

References SurrBasedMinimizer::alphaEta, SurrBasedLocalMinimizer::approxSubProbObj, SurrBasedMinimizer::constraint_violation(), Minimizer::constraintTol, SurrBasedMinimizer::eta, SurrBasedMinimizer::etaSequence, Iterator::iteratedModel, SurrBasedLocalMinimizer::meritFnType, SurrBasedLocalMinimizer::minimizeCycles, Minimizer::objective(), Iterator::outputLevel, SurrBasedLocalMinimizer::penaltyIterOffset, SurrBasedMinimizer::penaltyParameter, Model::primary_response_fn_sense(), and Model::primary_response_fn_weights().

Referenced by SurrBasedLocalMinimizer::compute_trust_region_ratio().

void approx_subprob_objective_eval	(	const Variables &	surrogate_vars,
		const Variables &	recast_vars,
		const Response &	surrogate_response,
		Response &	recast_response
	)

staticprotected

static function used to define the approximate subproblem objective.

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

Referenced by SurrBasedLocalMinimizer::initialize_sub_model().

void approx_subprob_constraint_eval	(	const Variables &	surrogate_vars,
		const Variables &	recast_vars,
		const Response &	surrogate_response,
		Response &	recast_response
	)

staticprotected

static function used to define the approximate subproblem constraints.

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

References Response::active_set_derivative_vector(), Response::active_set_request_vector(), SurrBasedLocalMinimizer::approxSubProbCon, SurrBasedLocalMinimizer::approxSubProbObj, Variables::continuous_variables(), Response::function_gradient(), Response::function_gradient_view(), Response::function_gradients(), Response::function_hessian(), Response::function_hessian_view(), Response::function_value(), Response::function_values(), Minimizer::numUserPrimaryFns, SurrBasedLocalMinimizer::sblmInstance, and SurrBasedLocalMinimizer::trust_region().

Referenced by SurrBasedLocalMinimizer::initialize_sub_model().

void hom_objective_eval	(	int &	mode,
		int &	n,
		double *	tau_and_x,
		double &	f,
		double *	grad_f,
		int &
	)

staticprotected

static function used by NPSOL as the objective function in the 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 .

Referenced by SurrBasedLocalMinimizer::relax_constraints().

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

staticprotected

static function used by NPSOL as the constraint function in the 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.

References Response::active_set(), SurrBasedLocalMinimizer::approxSubProbModel, Model::continuous_variables(), Model::current_response(), Model::evaluate(), Response::function_gradients(), Response::function_values(), SurrBasedLocalMinimizer::nonlinEqTargetsSlack, SurrBasedLocalMinimizer::nonlinIneqLowerBndsSlack, SurrBasedLocalMinimizer::nonlinIneqUpperBndsSlack, Minimizer::numNonlinearEqConstraints, Minimizer::numNonlinearIneqConstraints, ActiveSet::request_vector(), Model::response_size(), SurrBasedLocalMinimizer::sblmInstance, and SurrBasedLocalMinimizer::tau.

Referenced by SurrBasedLocalMinimizer::relax_constraints().

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

SurrBasedLocalMinimizer.hpp
SurrBasedLocalMinimizer.cpp

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