Solver class for the Pipal library. More...

#include <Solver.hxx>

Public Types
using	ProblemPtr = typename Problem<Real>::UniquePtr
using	ObjectiveFunc = typename ProblemWrapper<Real>::ObjectiveFunc
using	ObjectiveGradientFunc = typename ProblemWrapper<Real>::ObjectiveGradientFunc
using	ConstraintsFunc = typename ProblemWrapper<Real>::ConstraintsFunc
using	ConstraintsJacobianFunc = typename ProblemWrapper<Real>::ConstraintsJacobianFunc
using	LagrangianHessianFunc = typename ProblemWrapper<Real>::LagrangianHessianFunc
using	BoundsFunc = typename ProblemWrapper<Real>::BoundsFunc

Public Member Functions
	Solver ()=default
	Default constructor for the Pipal class.
	Solver (std::string const &name, ObjectiveFunc const &objective, ObjectiveGradientFunc const &objective_gradient, ConstraintsFunc const &constraints, ConstraintsJacobianFunc const &constraints_jacobian, LagrangianHessianFunc const &lagrangian_hessian, BoundsFunc const &primal_lower_bounds, BoundsFunc const &primal_upper_bounds, BoundsFunc const &constraints_lower_bounds, BoundsFunc const &constraints_upper_bounds)
	Constructor for the Pipal class.
	Solver (ProblemPtr &&problem)
	Constructor for the Pipal class (with a unique pointer to a Problem object).
	Solver (Solver const &)=delete
	Deleted copy constructor.
Solver &	operator= (Solver const &)=delete
	Deleted assignment operator.
	Solver (Solver &&)=delete
	Deleted move constructor.
Solver &	operator= (Solver &&)=delete
	Deleted move assignment operator.
	~Solver ()=default
	Destructor for the Pipal class.
void	problem (ProblemPtr &&problem)
	Set the problem to be solved using a unique pointer.
Problem< Real > const &	problem () const
	Get the problem being solved.
bool	verbose_mode () const
	Get the verbose mode.
void	verbose_mode (bool const t_verbose)
	Set the verbose mode.
bool	bfgs () const
	Get the BFGS mode.
void	bfgs (bool const t_bfgs)
	Set the BFGS mode.
Algorithm	algorithm () const
	Get the algorithm mode.
void	algorithm (Algorithm const t_algorithm)
	Set the algorithm mode.
void	tolerance (Real const t_tolerance)
	Set the convergence tolerance for the solver.
Real	tolerance () const
	Get the tolerance for convergence.
void	max_iterations (Integer const t_max_iterations)
	Set the maximum number of iterations for the solver.
Integer	max_iterations () const
	Get the maximum number of iterations.
bool	optimize (Vector< Real > const &x_guess, Vector< Real > &x_sol)
	Solves the optimization problem using the interior-point method.
void	getSolution (Vector< Real > &x, Vector< Real > &l)
	Extract a primal-dual solution in original ordering.

Private Member Functions
void	buildIterate ()
	Initialize an Iterate object for a given problem/input.
void	evalStep ()
	Compute the search direction for the current iterate.
void	updateParameters ()
	Update penalty and interior-point parameters based on KKT errors.
void	lineSearch ()
	Line-search driver.
void	bfgsUpdate (Vector< Real > const &s, Vector< Real > const &y)
	Browder-Broyden-Fletcher-Goldfarb-Shanno (BFGS) update for the Hessian approximation.
void	updateIterate ()
	Update the iterate after a trial step is accepted.
void	updatePoint ()
	Apply a step to the primal and dual variables of the iterate.
void	backtracking ()
	Backtracking line search.
void	evalFunctions ()
	Evaluate objective and constraint functions at the current iterate.
void	evalGradients ()
	Evaluate objective gradient and constraint Jacobian.
void	evalHessian ()
	Evaluate the Hessian of the Lagrangian and assemble internal H.
void	evalNewtonMatrix ()
	Assemble and (attempt to) factorize the Newton system matrix.
void	evalScalings ()
	Evaluate scaling multipliers for objective and constraints.
void	evalModels ()
	Evaluate model reductions and quality metric for a direction.
void	fractionToBoundary ()
	Fraction-to-boundary rule for primal and dual variables.
void	evalNewtonRhs ()
	Build the right-hand side vector for the Newton system.
void	evalSlacks ()
	Compute internal slack variables from current iterate.
void	evalMerit ()
	Compute the merit function value for the current iterate.
void	initNewtonMatrix ()
	Reserve and initialize the internal sparse Newton matrix structure.
void	resetDirection (Direction< Real > &d) const
	Reset a search direction to zero and initialize norms.
void	evalLambdaOriginal (Vector< Real > &l) const
	Reconstruct multipliers in the original variable/constraint space.
Real	evalViolation (Array< Real > const &cE, Array< Real > const &cI) const
	Compute the 1-norm feasibility violation from equality/inequality values.
void	evalNewtonStep ()
	Recover direction components from the Newton system solution.
void	evalTrialStep (Direction< Real > &v) const
	Store a trial step into another direction object.
Integer	checkTermination () const
	Check termination criteria for the solver.
Integer	fullStepCheck ()
	Full-step check for trial penalty parameters.
Integer	secondOrderCorrection ()
	Second-order correction (SOC).
void	evalXOriginal (Vector< Real > &x)
	Reconstruct the full primal vector in the original variable ordering.
void	setDirection (Vector< Real > const &dx, Vector< Real > const &dr1, Vector< Real > const &dr2, Vector< Real > const &ds1, Vector< Real > const &ds2, Vector< Real > const &dlE, Vector< Real > const &dlI, Real const dx_norm, Real const dl_norm)
	Populate a Direction object from its component vectors.
void	evalTrialSteps (Direction< Real > &d1, Direction< Real > &d2, Direction< Real > &d3)
	Compute and store directions for a few parameter combinations.
void	evalTrialStepCut ()
	Scale a trial step by the fraction-to-boundary values.
void	evalLinearCombination (Direction< Real > const &d1, Direction< Real > const &d2, Direction< Real > const &d3, Real const a1, Real const a2, Real const a3)
	Evaluate a linear combination of up to three directions.
Real	evalKKTError (Real const rho, Real const mu)
	Compute the infinity-norm of the KKT optimality vector.
void	evalKKTErrors ()
	Compute the three KKT error measures used by the solver.
void	setPrimals (Vector< Real > const &x, Array< Real > const &r1, Array< Real > const &r2, Array< Real > const &s1, Array< Real > const &s2, Array< Real > const &lE, Array< Real > const &lI, Real const f, Array< Real > const &cE, Array< Real > const &cI, Real const phi)
	Set primal/dual blocks and associated quantities on an iterate.
void	buildInput (std::string const &name, Vector< Real > const &x0, Vector< Real > const &bl, Vector< Real > const &bu, Vector< Real > const &cl, Vector< Real > const &cu)
	Build the input data for the solver.
void	evalInfeasibility (Iterate< Real > &z) const
	Compute scaled and unscaled feasibility violations.
void	resetMuMaxExp ()
	Reset maximum exponent used for mu increases to its default.
void	buildParameter (Algorithm t_algorithm)
	Initialize algorithm parameters.
void	setMuMaxExpZero ()
	Force mu exponent increases to use zero as maximum exponent.
void	setRho (Real const rho)
	Set penalty parameter rho.
void	setRhoLast (Real const rho)
	Set last (previous) penalty parameter value.
void	setMu (Real const mu)
	Set interior-point parameter `mu`.
void	evalDependent ()
	Evaluate quantities that depend on penalty/interior parameters.
void	resetCounter ()
	Reset all internal counters to zero.
void	incrementFactorizationCount ()
	Increment the matrix factorization counter.
void	incrementFunctionCount ()
	Increment the function evaluation counter.
void	incrementGradientCount ()
	Increment the gradient evaluation counter.
void	incrementHessianCount ()
	Increment the Hessian evaluation counter.
void	incrementIterationCount ()
	Increment the iteration counter.

Private Attributes
Counter	m_counter
Acceptance< Real >	m_acceptance
Input< Real >	m_input
Direction< Real >	m_direction
Iterate< Real >	m_iterate
Output< Real >	m_output
Parameter< Real >	m_parameter
ProblemPtr	m_problem
bool	m_verbose {false}
bool	m_bfgs {false}

Detailed Description

template<typename Real>
class Pipal::Solver< Real >

The Solver class provides an interface for solving the optimization problems using Frank E. Curtis Pipal algorithm. It utilizes the Problem class to define the optimization problem and implements various methods for solving it.

Template Parameters

Real	The floating-point type used for computations (e.g., float, double).

Member Typedef Documentation

◆ BoundsFunc

template<typename Real>

using Pipal::Solver< Real >::BoundsFunc = typename ProblemWrapper<Real>::BoundsFunc

◆ ConstraintsFunc

template<typename Real>

using Pipal::Solver< Real >::ConstraintsFunc = typename ProblemWrapper<Real>::ConstraintsFunc

◆ ConstraintsJacobianFunc

template<typename Real>

using Pipal::Solver< Real >::ConstraintsJacobianFunc = typename ProblemWrapper<Real>::ConstraintsJacobianFunc

◆ LagrangianHessianFunc

template<typename Real>

using Pipal::Solver< Real >::LagrangianHessianFunc = typename ProblemWrapper<Real>::LagrangianHessianFunc

◆ ObjectiveFunc

template<typename Real>

using Pipal::Solver< Real >::ObjectiveFunc = typename ProblemWrapper<Real>::ObjectiveFunc

◆ ObjectiveGradientFunc

template<typename Real>

using Pipal::Solver< Real >::ObjectiveGradientFunc = typename ProblemWrapper<Real>::ObjectiveGradientFunc

◆ ProblemPtr

template<typename Real>

using Pipal::Solver< Real >::ProblemPtr = typename Problem<Real>::UniquePtr

Constructor & Destructor Documentation

◆ Solver() [1/5]

template<typename Real>

Pipal::Solver< Real >::Solver ( )

default

Initializes the solver with default values for the objective, gradient, constraints, and Jacobian functions.

◆ Solver() [2/5]

template<typename Real>

Pipal::Solver< Real >::Solver	(	std::string const &	name,
		ObjectiveFunc const &	objective,
		ObjectiveGradientFunc const &	objective_gradient,
		ConstraintsFunc const &	constraints,
		ConstraintsJacobianFunc const &	constraints_jacobian,
		LagrangianHessianFunc const &	lagrangian_hessian,
		BoundsFunc const &	primal_lower_bounds,
		BoundsFunc const &	primal_upper_bounds,
		BoundsFunc const &	constraints_lower_bounds,
		BoundsFunc const &	constraints_upper_bounds )

inline

Initializes the solver with the provided objective, gradient, constraints, and Jacobian functions.

Parameters

[in]	name	Name of the optimization problem.
[in]	objective	Objective function handle.
[in]	objective_gradient	Gradient of the objective function handle.
[in]	constraints	Constraints function handle.
[in]	constraints_jacobian	Jacobian of the constraints function handle.
[in]	lagrangian_hessian	Hessian of the Lagrangian function handle.
[in]	primal_lower_bounds	Lower bounds on the primal variables handle.
[in]	primal_upper_bounds	Upper bounds on the primal variables handle.
[in]	constraints_lower_bounds	Lower bounds on the constraints handle.
[in]	constraints_upper_bounds	Upper bounds on the constraints handle.

◆ Solver() [3/5]

template<typename Real>

Pipal::Solver< Real >::Solver ( ProblemPtr && problem )

inline

Initializes the solver with the provided unique pointer to a Problem object.

Parameters

[in] problem The unique pointer to the Problem object to use.

Warning: The pointer is moved into the solver, so it should not be used after this call.

◆ Solver() [4/5]

template<typename Real>

Pipal::Solver< Real >::Solver ( Solver< Real > const & )

delete

Note: This class is not copyable.

◆ Solver() [5/5]

template<typename Real>

Pipal::Solver< Real >::Solver ( Solver< Real > && )

delete

Note: This class is not movable.

◆ ~Solver()

template<typename Real>

Pipal::Solver< Real >::~Solver ( )

default

Cleans up resources used by the solver.

Member Function Documentation

◆ algorithm() [1/2]

template<typename Real>

Algorithm Pipal::Solver< Real >::algorithm ( ) const

inline

Returns: The algorithm mode.

◆ algorithm() [2/2]

template<typename Real>

void Pipal::Solver< Real >::algorithm ( Algorithm const t_algorithm )

inline

This method allows the user to specify the algorithm mode, which can be either CONSERVATIVE or ADAPTIVE.

Parameters

[in] t_algorithm The algorithm mode.

◆ backtracking()

template<typename Real>

void Pipal::Solver< Real >::backtracking ( )

private

Performs a backtracking Armijo line search on the merit function. The routine updates the trial primal/dual variables using the candidate direction and the current acceptance object. On success the iterate is restored to the accepted trial point; otherwise the steplength is reduced until the Armijo condition or the fraction-to-boundary constraint prevents further reductions.

◆ bfgs() [1/2]

template<typename Real>

bool Pipal::Solver< Real >::bfgs ( ) const

inline

Returns: The BFGS mode.

◆ bfgs() [2/2]

template<typename Real>

void Pipal::Solver< Real >::bfgs ( bool const t_bfgs )

inline

Parameters

[in] t_bfgs The BFGS mode.

◆ bfgsUpdate()

template<typename Real>

void Pipal::Solver< Real >::bfgsUpdate	(	Vector< Real > const &	s,
		Vector< Real > const &	y )

private

This method updates the Hessian approximation using the Browder-Broyden-Fletcher-Goldfarb-Shanno (BFGS) formula*

\[ \mathbf{B}_{k+1} = \mathbf{B}_{k} - \displaystyle\frac{(\mathbf{B}_{k}\mathbf{s}_{k})( \mathbf{B}_{k}\mathbf{s}_{k}^\top)}{\mathbf{s}_{k}^\top \mathbf{B}_{k}\mathbf{s}_{k}} + \displaystyle\frac{\mathbf{y}\mathbf{y}^\top)}{\mathbf{y}^\top\mathbf{s}_{k}} \]

where \(B\) is the current Hessian approximation, \(s\) is the step taken, and \(y\) is the gradient difference.

Note: The condition \(y^\top s > 0\) must be satisfied for the update to be valid.

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[in]	s	Step taken in primal variables.
[in]	y	Difference in gradients.

Returns: Updated Hessian approximation.

◆ buildInput()

template<typename Real>

void Pipal::Solver< Real >::buildInput	(	std::string const &	name,
		Vector< Real > const &	x0,
		Vector< Real > const &	bl,
		Vector< Real > const &	bu,
		Vector< Real > const &	cl,
		Vector< Real > const &	cu )

private

Parameters

[in]	name	Problem name.
[in]	x0	Initial guess for the solution.
[in]	bl	Lower bounds for the variables.
[in]	bu	Upper bounds for the variables.
[in]	cl	Lower bounds for the constraints.
[in]	cu	Upper bounds for the constraints.

◆ buildIterate()

template<typename Real>

void Pipal::Solver< Real >::buildIterate ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ buildParameter()

template<typename Real>

void Pipal::Solver< Real >::buildParameter ( Algorithm t_algorithm )

inlineprivate

Parameters

[in] t_algorithm Algorithm selection enumerator.

◆ checkTermination()

template<typename Real>

Integer Pipal::Solver< Real >::checkTermination ( ) const

private

Evaluates optimality/feasibility/iteration-count/bounds error conditions and returns the termination code used by the solver.

Template Parameters

Real	Floating-point type used by the algorithm.

Returns: An integer termination code (0 = continue, 1..5 = specific exits).

◆ evalDependent()

template<typename Real>

void Pipal::Solver< Real >::evalDependent ( )

inlineprivate

Runs slack, merit and KKT-error evaluations that are functions of the current penalty and interior-point parameters.

◆ evalFunctions()

template<typename Real>

void Pipal::Solver< Real >::evalFunctions ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalGradients()

template<typename Real>

void Pipal::Solver< Real >::evalGradients ( )

private

Calls the problem-provided gradient/jacobian functions in the original space, maps the results into the internal compressed representations and applies scaling. Increments gradient counters and handles exceptions.

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalHessian()

template<typename Real>

void Pipal::Solver< Real >::evalHessian ( )

private

Calls the problem's Hessian-of-Lagrangian routine (with multipliers and primal variables in the original space), maps blocks into the internal sparse Hessian and rescales according to penalization and scaling factors.

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalInfeasibility()

template<typename Real>

void Pipal::Solver< Real >::evalInfeasibility ( Iterate< Real > & z ) const

inlineprivate

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[in] z Current iterate.

◆ evalKKTError()

template<typename Real>

Real Pipal::Solver< Real >::evalKKTError	(	Real const	rho,
		Real const	mu )

private

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[in]	rho	Current penalty parameter.
[in]	mu	Current interior-point parameter.

Returns: The infinity-norm of the KKT optimality vector.

◆ evalKKTErrors()

template<typename Real>

void Pipal::Solver< Real >::evalKKTErrors ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalLambdaOriginal()

template<typename Real>

void Pipal::Solver< Real >::evalLambdaOriginal ( Vector< Real > & l ) const

private

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[out] l Vector to store multipliers in original space.

◆ evalLinearCombination()

template<typename Real>

void Pipal::Solver< Real >::evalLinearCombination	(	Direction< Real > const &	d1,
		Direction< Real > const &	d2,
		Direction< Real > const &	d3,
		Real const	a1,
		Real const	a2,
		Real const	a3 )

private

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[in]	d1	First direction.
[in]	d2	Second direction.
[in]	d3	Third direction.
[in]	a1	Scalar multiplier for the first direction.
[in]	a2	Scalar multiplier for the second direction.
[in]	a3	Scalar multiplier for the third direction.

◆ evalMerit()

template<typename Real>

void Pipal::Solver< Real >::evalMerit ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalModels()

template<typename Real>

void Pipal::Solver< Real >::evalModels ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalNewtonMatrix()

template<typename Real>

void Pipal::Solver< Real >::evalNewtonMatrix ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalNewtonRhs()

template<typename Real>

void Pipal::Solver< Real >::evalNewtonRhs ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalNewtonStep()

template<typename Real>

void Pipal::Solver< Real >::evalNewtonStep ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalScalings()

template<typename Real>

void Pipal::Solver< Real >::evalScalings ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalSlacks()

template<typename Real>

void Pipal::Solver< Real >::evalSlacks ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalStep()

template<typename Real>

void Pipal::Solver< Real >::evalStep ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalTrialStep()

template<typename Real>

void Pipal::Solver< Real >::evalTrialStep ( Direction< Real > & v ) const

private

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[out] v Destination direction that will contain the trial step.

◆ evalTrialStepCut()

template<typename Real>

void Pipal::Solver< Real >::evalTrialStepCut ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ evalTrialSteps()

template<typename Real>

void Pipal::Solver< Real >::evalTrialSteps	(	Direction< Real > &	d1,
		Direction< Real > &	d2,
		Direction< Real > &	d3 )

private

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[out]	d1	Direction for the first parameter combination.
[out]	d2	Direction for the second parameter combination.
[out]	d3	Direction for the third parameter combination.

◆ evalViolation()

template<typename Real>

Real Pipal::Solver< Real >::evalViolation	(	Array< Real > const &	cE,
		Array< Real > const &	cI ) const

private

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[in]	cE	Equality constraint values.
[in]	cI	Inequality constraint values.

Returns: The 1-norm feasibility violation.

◆ evalXOriginal()

template<typename Real>

void Pipal::Solver< Real >::evalXOriginal ( Vector< Real > & x )

private

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[out] x Vector to store primal variables in original space.

◆ fractionToBoundary()

template<typename Real>

void Pipal::Solver< Real >::fractionToBoundary ( )

private

Computes the maximum allowable primal and dual step fractions that keep interior-point slacks and multipliers within their prescribed bounds. The computed values are stored in the a.p0 (initial primal fraction), a.p (primal steplength) and a.d (dual steplength).

Template Parameters

Real	Floating-point type used by the algorithm.

◆ fullStepCheck()

template<typename Real>

Integer Pipal::Solver< Real >::fullStepCheck ( )

private

Attempts full steps for a sequence of trial penalty parameters, verifying the Armijo condition on the merit. If a full step satisfies the acceptance condition the routine returns 1 and the iterate is left at the accepted trial point; otherwise the penalty parameter is decreased and the process repeats.

Template Parameters

Real	Floating-point type used by the algorithm.

Returns: 1 if a full step was accepted, 0 otherwise.

◆ getSolution()

template<typename Real>

void Pipal::Solver< Real >::getSolution	(	Vector< Real > &	x,
		Vector< Real > &	l )

inline

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[out]	x	Vector to store primal variables in original space.
[out]	l	Vector to store multipliers in original space.

◆ incrementFactorizationCount()

template<typename Real>

void Pipal::Solver< Real >::incrementFactorizationCount ( )

inlineprivate

◆ incrementFunctionCount()

template<typename Real>

void Pipal::Solver< Real >::incrementFunctionCount ( )

inlineprivate

◆ incrementGradientCount()

template<typename Real>

void Pipal::Solver< Real >::incrementGradientCount ( )

inlineprivate

◆ incrementHessianCount()

template<typename Real>

void Pipal::Solver< Real >::incrementHessianCount ( )

inlineprivate

◆ incrementIterationCount()

template<typename Real>

void Pipal::Solver< Real >::incrementIterationCount ( )

inlineprivate

◆ initNewtonMatrix()

template<typename Real>

void Pipal::Solver< Real >::initNewtonMatrix ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ lineSearch()

template<typename Real>

void Pipal::Solver< Real >::lineSearch ( )

private

Runs the fraction-to-boundary rule, full-step check, second-order correction and backtracking as needed to find an acceptable trial step. The acceptance object is updated with the final chosen step.

Template Parameters

Real	Floating-point type used by the algorithm.

◆ max_iterations() [1/2]

template<typename Real>

Integer Pipal::Solver< Real >::max_iterations ( ) const

inline

Returns: The maximum number of iterations.

◆ max_iterations() [2/2]

template<typename Real>

void Pipal::Solver< Real >::max_iterations ( Integer const t_max_iterations )

inline

This method allows the user to specify the maximum number of iterations the solver will perform before stopping.

Parameters

[in] t_max_iterations The maximum number of iterations.

◆ operator=() [1/2]

template<typename Real>

Solver & Pipal::Solver< Real >::operator= ( Solver< Real > && )

delete

Note: This class is not movable.

◆ operator=() [2/2]

template<typename Real>

Solver & Pipal::Solver< Real >::operator= ( Solver< Real > const & )

delete

Note: This class is not assignable.

◆ optimize()

template<typename Real>

bool Pipal::Solver< Real >::optimize	(	Vector< Real > const &	x_guess,
		Vector< Real > &	x_sol )

inline

This method implements the interior-point algorithm to solve the optimization problem defined by the objective function, constraints, and their respective gradients and Jacobians.

Parameters

[in]	x_guess	Initial guess for the optimization variables.
[out]	x_sol	Solution vector.

Returns: True if the optimization was successful, false otherwise.

◆ problem() [1/2]

template<typename Real>

Problem< Real > const & Pipal::Solver< Real >::problem ( ) const

inline

Returns: A reference to the problem.

◆ problem() [2/2]

template<typename Real>

void Pipal::Solver< Real >::problem ( ProblemPtr && problem )

inline

This method allows the user to specify the problem to be solved using a unique pointer.

Parameters

[in] problem The unique pointer to the problem to set.

◆ resetCounter()

template<typename Real>

void Pipal::Solver< Real >::resetCounter ( )

inlineprivate

◆ resetDirection()

template<typename Real>

void Pipal::Solver< Real >::resetDirection ( Direction< Real > & d ) const

private

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[in] d Direction object to reset.

◆ resetMuMaxExp()

template<typename Real>

void Pipal::Solver< Real >::resetMuMaxExp ( )

inlineprivate

Template Parameters

Real	Floating-point type used by the algorithm.

◆ secondOrderCorrection()

template<typename Real>

Integer Pipal::Solver< Real >::secondOrderCorrection ( )

private

Attempts a second-order correction to improve feasibility when the trial step fails the Armijo condition (or other checks). The routine evaluates a corrected Newton step and tests acceptance similarly to the main line-search path.

Template Parameters

Real	Floating-point type used by the algorithm.

Returns: 0 if SOC not accepted, 1 if first acceptance criterion met, 2 if SOC accepted.

◆ setDirection()

template<typename Real>

void Pipal::Solver< Real >::setDirection	(	Vector< Real > const &	dx,
		Vector< Real > const &	dr1,
		Vector< Real > const &	dr2,
		Vector< Real > const &	ds1,
		Vector< Real > const &	ds2,
		Vector< Real > const &	dlE,
		Vector< Real > const &	dlI,
		Real const	dx_norm,
		Real const	dl_norm )

private

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[in]	dx	Primal component of the direction.
[in]	dr1	Equality slack direction (first part).
[in]	dr2	Equality slack direction (second part).
[in]	ds1	Inequality slack direction (first part).
[in]	ds2	Inequality slack direction (second part).
[in]	dlE	Equality multipliers direction.
[in]	dlI	Inequality multipliers direction.
[in]	dx_norm	Norm of the primal direction (precomputed).
[in]	dl_norm	Norm of the dual direction (precomputed).

◆ setMu()

template<typename Real>

void Pipal::Solver< Real >::setMu ( Real const mu )

inlineprivate

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[in] mu New interior-point parameter value.

◆ setMuMaxExpZero()

template<typename Real>

void Pipal::Solver< Real >::setMuMaxExpZero ( )

inlineprivate

◆ setPrimals()

template<typename Real>

void Pipal::Solver< Real >::setPrimals	(	Vector< Real > const &	x,
		Array< Real > const &	r1,
		Array< Real > const &	r2,
		Array< Real > const &	s1,
		Array< Real > const &	s2,
		Array< Real > const &	lE,
		Array< Real > const &	lI,
		Real const	f,
		Array< Real > const &	cE,
		Array< Real > const &	cI,
		Real const	phi )

private

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[in]	x	Primal variable vector.
[in]	r1	Equality constraint slack variables (lower).
[in]	r2	Equality constraint slack variables (upper).
[in]	s1	Inequality constraint slack variables (lower).
[in]	s2	Inequality constraint slack variables (upper).
[in]	lE	Equality constraint multipliers.
[in]	lI	Inequality constraint multipliers.
[in]	f	Objective function value.
[in]	cE	Equality constraint values.
[in]	cI	Inequality constraint values.
[in]	phi	Merit function value.

◆ setRho()

template<typename Real>

void Pipal::Solver< Real >::setRho ( Real const rho )

inlineprivate

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[in] rho New penalty parameter value.

◆ setRhoLast()

template<typename Real>

void Pipal::Solver< Real >::setRhoLast ( Real const rho )

inlineprivate

Template Parameters

Real	Floating-point type used by the algorithm.

Parameters

[in] rho New last penalty parameter value.

◆ tolerance() [1/2]

template<typename Real>

Real Pipal::Solver< Real >::tolerance ( ) const

inline

Returns: The tolerance for convergence.

◆ tolerance() [2/2]

template<typename Real>

void Pipal::Solver< Real >::tolerance ( Real const t_tolerance )

inline

This method allows the user to specify the tolerance for convergence. The solver will stop when the residuals are below this tolerance.

Parameters

[in] t_tolerance The convergence tolerance.

◆ updateIterate()

template<typename Real>

void Pipal::Solver< Real >::updateIterate ( )

private

Applies the accepted step to the iterate, recomputes infeasibility and gradients and updates parameter memory used for adaptive strategies.

Template Parameters

Real	Floating-point type used by the algorithm.

◆ updateParameters()

template<typename Real>

void Pipal::Solver< Real >::updateParameters ( )

private

Adjusts rho and mu using the solver's adaptive rules to drive optimality and feasibility towards the desired tolerances.

Template Parameters

Real	Floating-point type used by the algorithm.

◆ updatePoint()

template<typename Real>

void Pipal::Solver< Real >::updatePoint ( )

private

Template Parameters

Real	Floating-point type used by the algorithm.

◆ verbose_mode() [1/2]

template<typename Real>

bool Pipal::Solver< Real >::verbose_mode ( ) const

inline

Returns: The verbose mode.

◆ verbose_mode() [2/2]

template<typename Real>

void Pipal::Solver< Real >::verbose_mode ( bool const t_verbose )

inline

Parameters

[in] t_verbose The verbose mode.

Member Data Documentation

◆ m_acceptance

template<typename Real>

Acceptance<Real> Pipal::Solver< Real >::m_acceptance

private

Acceptance criteria for trial points.

◆ m_bfgs

template<typename Real>

bool Pipal::Solver< Real >::m_bfgs {false}

private

BFGS update flag.

◆ m_counter

template<typename Real>

Counter Pipal::Solver< Real >::m_counter

private

Internal counters for solver statistics.

◆ m_direction

template<typename Real>

Direction<Real> Pipal::Solver< Real >::m_direction

private

Current search direction of the solver.

◆ m_input

template<typename Real>

Input<Real> Pipal::Solver< Real >::m_input

private

Input structure for the solver.

◆ m_iterate

template<typename Real>

Iterate<Real> Pipal::Solver< Real >::m_iterate

private

Current iterate of the solver.

◆ m_output

template<typename Real>

Output<Real> Pipal::Solver< Real >::m_output

private

Output class for managing solver output.

◆ m_parameter

template<typename Real>

Parameter<Real> Pipal::Solver< Real >::m_parameter

private

Internal parameters for the solver algorithm.

◆ m_problem

template<typename Real>

ProblemPtr Pipal::Solver< Real >::m_problem

private

Problem object pointer.

◆ m_verbose

template<typename Real>

bool Pipal::Solver< Real >::m_verbose {false}

private

Verbosity flag.

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

include/Pipal/Solver.hxx
include/Pipal/Acceptance.hxx
include/Pipal/Direction.hxx
include/Pipal/Input.hxx
include/Pipal/Iterate.hxx

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ BoundsFunc

◆ ConstraintsFunc

◆ ConstraintsJacobianFunc

◆ LagrangianHessianFunc

◆ ObjectiveFunc

◆ ObjectiveGradientFunc

◆ ProblemPtr

Constructor & Destructor Documentation

◆ Solver() [1/5]

◆ Solver() [2/5]

◆ Solver() [3/5]

◆ Solver() [4/5]

◆ Solver() [5/5]

◆ ~Solver()

Member Function Documentation

◆ algorithm() [1/2]

◆ algorithm() [2/2]

◆ backtracking()

◆ bfgs() [1/2]

◆ bfgs() [2/2]

◆ bfgsUpdate()

◆ buildInput()

◆ buildIterate()

◆ buildParameter()

◆ checkTermination()

◆ evalDependent()

◆ evalFunctions()

◆ evalGradients()

◆ evalHessian()

◆ evalInfeasibility()

◆ evalKKTError()

◆ evalKKTErrors()

◆ evalLambdaOriginal()

◆ evalLinearCombination()

◆ evalMerit()

◆ evalModels()

◆ evalNewtonMatrix()

◆ evalNewtonRhs()

◆ evalNewtonStep()

◆ evalScalings()

◆ evalSlacks()

◆ evalStep()

◆ evalTrialStep()

◆ evalTrialStepCut()

◆ evalTrialSteps()

◆ evalViolation()

◆ evalXOriginal()

◆ fractionToBoundary()

◆ fullStepCheck()

◆ getSolution()

◆ incrementFactorizationCount()

◆ incrementFunctionCount()

◆ incrementGradientCount()

◆ incrementHessianCount()

◆ incrementIterationCount()

◆ initNewtonMatrix()

◆ lineSearch()

◆ max_iterations() [1/2]

◆ max_iterations() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ optimize()

◆ problem() [1/2]

◆ problem() [2/2]

◆ resetCounter()

◆ resetDirection()

◆ resetMuMaxExp()

◆ secondOrderCorrection()

◆ setDirection()

◆ setMu()

◆ setMuMaxExpZero()

◆ setPrimals()

◆ setRho()

◆ setRhoLast()