Detailed Description

template<Config Conf>
struct alpaqa::detail::PANOCHelpers< Conf >

Definition at line 17 of file panoc-helpers.tpp.

Collaboration diagram for PANOCHelpers< Conf >:

Public Types
using	Problem = alpaqa::TypeErasedProblem< config_t >

using	Box = alpaqa::Box< config_t >

Static Public Member Functions
static void	calc_err_z (const Problem &p, crvec x̂, crvec y, crvec Σ, rvec err_z)
	Calculate the error between ẑ and g(x).

static bool	stop_crit_requires_grad_ψx̂ (PANOCStopCrit crit)

static real_t	calc_error_stop_crit (const Problem &problem, PANOCStopCrit crit, crvec pₖ, real_t γ, crvec xₖ, crvec x̂ₖ, crvec ŷₖ, crvec grad_ψₖ, crvec grad_̂ψₖ, rvec work_n1, rvec work_n2)
	Compute the ε from the stopping criterion, see PANOCStopCrit.

static real_t	descent_lemma (const Problem &problem, real_t rounding_tolerance, real_t L_max, crvec xₖ, real_t ψₖ, crvec grad_ψₖ, crvec y, crvec Σ, rvec x̂ₖ, rvec pₖ, rvec ŷx̂ₖ, real_t &ψx̂ₖ, real_t &norm_sq_pₖ, real_t &grad_ψₖᵀpₖ, real_t &Lₖ, real_t &γₖ)
	Increase the estimate of the Lipschitz constant of the objective gradient and decrease the step size until quadratic upper bound or descent lemma is satisfied:

template<class ParamsT , class DurationT >
static SolverStatus	check_all_stop_conditions (const ParamsT &params, const InnerSolveOptions< config_t > &opts, DurationT time_elapsed, unsigned iteration, const AtomicStopSignal &stop_signal, real_t εₖ, unsigned no_progress)
	Check all stop conditions (required tolerance reached, out of time, maximum number of iterations exceeded, interrupted by user, infinite iterate, no progress made)

static void	calc_augmented_lagrangian_hessian_prod_fd (const Problem &problem, crvec xₖ, crvec y, crvec Σ, crvec grad_ψ, crvec v, rvec Hv, rvec work_n1, rvec work_n2, rvec work_m)
	Compute the Hessian matrix of the augmented Lagrangian function multiplied by the given vector, using finite differences.

static real_t	initial_lipschitz_estimate (const Problem &problem, crvec x, crvec y, crvec Σ, real_t ε, real_t δ, real_t L_min, real_t L_max, real_t &ψ, rvec grad_ψ, rvec work_x, rvec work_grad_ψ, rvec work_n, rvec work_m)
	Estimate the Lipschitz constant of the gradient \( \nabla \psi \) using finite differences.

static real_t	initial_lipschitz_estimate (const Problem &problem, crvec xₖ, crvec y, crvec Σ, real_t ε, real_t δ, real_t L_min, real_t L_max, rvec grad_ψ, rvec work_n1, rvec work_n2, rvec work_n3, rvec work_m)
	Estimate the Lipschitz constant of the gradient \( \nabla \psi \) using finite differences.

Member Typedef Documentation

◆ Problem

template<Config Conf>

using Problem = alpaqa::TypeErasedProblem<config_t>

Definition at line 19 of file panoc-helpers.tpp.

◆ Box

template<Config Conf>

using Box = alpaqa::Box<config_t>

Definition at line 20 of file panoc-helpers.tpp.

Member Function Documentation

◆ calc_err_z()

template<Config Conf>

static void calc_err_z	(	const Problem &	p,
		crvec	x̂,
		crvec	y,
		crvec	Σ,
		rvec	err_z
	)

inlinestatic

Calculate the error between ẑ and g(x).

\[ \hat{z}^k = \Pi_D\left(g(x^k) + \Sigma^{-1}y\right) \]

Parameters

[in]	p	Problem description
[in]	x̂	Decision variable \( \hat{x} \)
[in]	y	Lagrange multipliers \( y \)
[in]	Σ	Penalty weights \( \Sigma \)
[out]	err_z	\( g(\hat{x}) - \hat{z} \)

Definition at line 24 of file panoc-helpers.tpp.

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◆ stop_crit_requires_grad_ψx̂()

template<Config Conf>

static bool stop_crit_requires_grad_ψx̂ ( PANOCStopCrit crit )

inlinestatic

Definition at line 44 of file panoc-helpers.tpp.

◆ calc_error_stop_crit()

template<Config Conf>

static real_t calc_error_stop_crit	(	const Problem &	problem,
		PANOCStopCrit	crit,
		crvec	pₖ,
		real_t	γ,
		crvec	xₖ,
		crvec	x̂ₖ,
		crvec	ŷₖ,
		crvec	grad_ψₖ,
		crvec	grad_̂ψₖ,
		rvec	work_n1,
		rvec	work_n2
	)

inlinestatic

Compute the ε from the stopping criterion, see PANOCStopCrit.

Parameters

[in]	problem	Problem description
[in]	crit	What stoppint criterion to use
[in]	pₖ	Projected gradient step \( \hat x^k - x^k \)
[in]	γ	Step size
[in]	xₖ	Current iterate
[in]	x̂ₖ	Current iterate after projected gradient step
[in]	ŷₖ	Candidate Lagrange multipliers
[in]	grad_ψₖ	Gradient in \( x^k \)
[in]	grad_̂ψₖ	Gradient in \( \hat x^k \)
	work_n1	Workspace of dimension n
	work_n2	Workspace of dimension n

Definition at line 62 of file panoc-helpers.tpp.

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◆ descent_lemma()

template<Config Conf>

static real_t descent_lemma	(	const Problem &	problem,
		real_t	rounding_tolerance,
		real_t	L_max,
		crvec	xₖ,
		real_t	ψₖ,
		crvec	grad_ψₖ,
		crvec	y,
		crvec	Σ,
		rvec	x̂ₖ,
		rvec	pₖ,
		rvec	ŷx̂ₖ,
		real_t &	ψx̂ₖ,
		real_t &	norm_sq_pₖ,
		real_t &	grad_ψₖᵀpₖ,
		real_t &	Lₖ,
		real_t &	γₖ
	)

inlinestatic

Increase the estimate of the Lipschitz constant of the objective gradient and decrease the step size until quadratic upper bound or descent lemma is satisfied:

\[ \psi(x + p) \le \psi(x) + \nabla\psi(x)^\top p + \frac{L}{2} \|p\|^2 \]

The projected gradient iterate \( \hat x^k \) and step \( p^k \) are updated with the new step size \( \gamma^k \), and so are other quantities that depend on them, such as \( \nabla\psi(x^k)^\top p^k \) and \( \|p\|^2 \). The intermediate vector \( \hat y(x^k) \) can be used to compute the gradient \( \nabla\psi(\hat x^k) \) or to update the Lagrange multipliers.

Returns: The original step size, before it was reduced by this function.

Parameters

[in]	problem	Problem description
[in]	rounding_tolerance	Tolerance used to ignore rounding errors when the function \( \psi(x) \) is relatively flat or the step size is very small, which could cause \( \psi(x^k) < \psi(\hat x^k) \), which is mathematically impossible but could occur in finite precision floating point arithmetic.
[in]	L_max	Maximum allowed Lipschitz constant estimate (prevents infinite loop if function or derivatives are discontinuous, and keeps step size bounded away from zero).
[in]	xₖ	Current iterate \( x^k \)
[in]	ψₖ	Objective function \( \psi(x^k) \)
[in]	grad_ψₖ	Gradient of objective \( \nabla\psi(x^k) \)
[in]	y	Lagrange multipliers \( y \)
[in]	Σ	Penalty weights \( \Sigma \)
[out]	x̂ₖ	Projected gradient iterate \( \hat x^k \)
[out]	pₖ	Projected gradient step \( p^k \)
[out]	ŷx̂ₖ	Intermediate vector \( \hat y(\hat x^k) \)
[in,out]	ψx̂ₖ	Objective function \( \psi(\hat x^k) \)
[in,out]	norm_sq_pₖ	Squared norm of the step \( \left\\| p^k \right\\|^2 \)
[in,out]	grad_ψₖᵀpₖ	Gradient of objective times step \( \nabla\psi(x^k)^\top p^k\)
[in,out]	Lₖ	Lipschitz constant estimate \( L_{\nabla\psi}^k \)
[in,out]	γₖ	Step size \( \gamma^k \)

Definition at line 152 of file panoc-helpers.tpp.

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◆ check_all_stop_conditions()

template<Config Conf>

template<class ParamsT , class DurationT >

static SolverStatus check_all_stop_conditions	(	const ParamsT &	params,
		const InnerSolveOptions< config_t > &	opts,
		DurationT	time_elapsed,
		unsigned	iteration,
		const AtomicStopSignal &	stop_signal,
		real_t	εₖ,
		unsigned	no_progress
	)

inlinestatic

Check all stop conditions (required tolerance reached, out of time, maximum number of iterations exceeded, interrupted by user, infinite iterate, no progress made)

Parameters

[in]	params	Parameters including `max_iter`, `max_time` and `max_no_progress`
[in]	opts	Options for the current solve
[in]	time_elapsed	Time elapsed since the start of the algorithm
[in]	iteration	The current iteration number
[in]	stop_signal	A stop signal for the user to interrupt the algorithm
[in]	εₖ	Tolerance of the current iterate
[in]	no_progress	The number of successive iterations no progress was made

Definition at line 217 of file panoc-helpers.tpp.

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◆ calc_augmented_lagrangian_hessian_prod_fd()

template<Config Conf>

static void calc_augmented_lagrangian_hessian_prod_fd	(	const Problem &	problem,
		crvec	xₖ,
		crvec	y,
		crvec	Σ,
		crvec	grad_ψ,
		crvec	v,
		rvec	Hv,
		rvec	work_n1,
		rvec	work_n2,
		rvec	work_m
	)

inlinestatic

Compute the Hessian matrix of the augmented Lagrangian function multiplied by the given vector, using finite differences.

\[ \nabla^2_{xx} L_\Sigma(x, y)\, v \approx \frac{\nabla_x L_\Sigma(x+hv, y) - \nabla_x L_\Sigma(x, y)}{h} \]

Parameters

[in]	problem	Problem description
[in]	xₖ	Current iterate \( x^k \)
[in]	y	Lagrange multipliers \( y \)
[in]	Σ	Penalty weights \( \Sigma \)
[in]	grad_ψ	Gradient \( \nabla \psi(x^k) \)
[in]	v	Vector to multiply with the Hessian
[out]	Hv	Hessian-vector product
	work_n1	Dimension n
	work_n2	Dimension n
	work_m	Dimension m

Definition at line 256 of file panoc-helpers.tpp.

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◆ initial_lipschitz_estimate() [1/2]

template<Config Conf>

static real_t initial_lipschitz_estimate	(	const Problem &	problem,
		crvec	x,
		crvec	y,
		crvec	Σ,
		real_t	ε,
		real_t	δ,
		real_t	L_min,
		real_t	L_max,
		real_t &	ψ,
		rvec	grad_ψ,
		rvec	work_x,
		rvec	work_grad_ψ,
		rvec	work_n,
		rvec	work_m
	)

inlinestatic

Estimate the Lipschitz constant of the gradient \( \nabla \psi \) using finite differences.

Parameters

[in]	problem	Problem description
[in]	x	Current iterate \( x^k \)
[in]	y	Lagrange multipliers \( y \)
[in]	Σ	Penalty weights \( \Sigma \)
[in]	ε	Finite difference step size relative to x
[in]	δ	Minimum absolute finite difference step size
[in]	L_min	Minimum allowed Lipschitz estimate.
[in]	L_max	Maximum allowed Lipschitz estimate.
[out]	ψ	\( \psi(x^k) \)
[out]	grad_ψ	Gradient \( \nabla \psi(x^k) \)
	work_x	Dimension n
	work_grad_ψ	Dimension n
	work_n	Dimension n
	work_m	Dimension m

Definition at line 289 of file panoc-helpers.tpp.

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◆ initial_lipschitz_estimate() [2/2]

template<Config Conf>

static real_t initial_lipschitz_estimate	(	const Problem &	problem,
		crvec	xₖ,
		crvec	y,
		crvec	Σ,
		real_t	ε,
		real_t	δ,
		real_t	L_min,
		real_t	L_max,
		rvec	grad_ψ,
		rvec	work_n1,
		rvec	work_n2,
		rvec	work_n3,
		rvec	work_m
	)

inlinestatic

Estimate the Lipschitz constant of the gradient \( \nabla \psi \) using finite differences.

Parameters

[in]	problem	Problem description
[in]	xₖ	Current iterate \( x^k \)
[in]	y	Lagrange multipliers \( y \)
[in]	Σ	Penalty weights \( \Sigma \)
[in]	ε	Finite difference step size relative to xₖ
[in]	δ	Minimum absolute finite difference step size
[in]	L_min	Minimum allowed Lipschitz estimate.
[in]	L_max	Maximum allowed Lipschitz estimate.
[out]	grad_ψ	Gradient \( \nabla \psi(x^k) \)
	work_n1	Dimension n
	work_n2	Dimension n
	work_n3	Dimension n
	work_m	Dimension m

Definition at line 339 of file panoc-helpers.tpp.

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

src/alpaqa/include/alpaqa/implementation/inner/panoc-helpers.tpp

Detailed Description

Public Types

Static Public Member Functions

Member Typedef Documentation

◆ Problem

◆ Box

Member Function Documentation

◆ calc_err_z()

◆ stop_crit_requires_grad_ψx̂()

◆ calc_error_stop_crit()

◆ descent_lemma()

◆ check_all_stop_conditions()

◆ calc_augmented_lagrangian_hessian_prod_fd()

◆ initial_lipschitz_estimate() [1/2]

◆ initial_lipschitz_estimate() [2/2]