PANOCHelpers< Conf > Struct Template Reference

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 $\mathrm{\nabla }\psi$ 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 $\mathrm{\nabla }\psi$ 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).

$${\hat{z}}^k={\mathrm{\Pi }}_D(g(x^k)+{\mathrm{\Sigma }}^{-1}y)$$

Parameters

[in]	p	Problem description
[in]	x̂	Decision variable $\hat{x}$
[in]	y	Lagrange multipliers $y$
[in]	Σ	Penalty weights $\mathrm{\Sigma }$
[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:

$$\psi (x+p)\le \psi (x)+\mathrm{\nabla }\psi (x{)}^{\mathrm{\top }}p+\frac{L}{2}\Vert p{\Vert }^2$$

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 $\mathrm{\nabla }\psi (x^k{)}^{\mathrm{\top }}{p}^k$ and $\Vert p{\Vert }^2$. The intermediate vector $\hat{y}(x^k)$ can be used to compute the gradient $\mathrm{\nabla }\psi ({\hat{x}}^k)$ 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 $\mathrm{\nabla }\psi (x^k)$
[in]	y	Lagrange multipliers $y$
[in]	Σ	Penalty weights $\mathrm{\Sigma }$
[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 ${\Vert p^k\Vert }^2$
[in,out]	grad_ψₖᵀpₖ	Gradient of objective times step $\mathrm{\nabla }\psi (x^k{)}^{\mathrm{\top }}{p}^k$
[in,out]	Lₖ	Lipschitz constant estimate $L_{\mathrm{\nabla }\psi }^k$
[in,out]	γₖ	Step size ${\gamma }^k$

Definition at line 151 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 216 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.

$${\mathrm{\nabla }}_{xx}^2{L}_{\mathrm{\Sigma }}(x,y)v\approx \frac{{\mathrm{\nabla }}_x{L}_{\mathrm{\Sigma }}(x+hv,y)-{\mathrm{\nabla }}_x{L}_{\mathrm{\Sigma }}(x,y)}{h}$$

Parameters

[in]	problem	Problem description
[in]	xₖ	Current iterate $x^k$
[in]	y	Lagrange multipliers $y$
[in]	Σ	Penalty weights $\mathrm{\Sigma }$
[in]	grad_ψ	Gradient $\mathrm{\nabla }\psi (x^k)$
[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 255 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 $\mathrm{\nabla }\psi$ using finite differences.

Parameters

[in]	problem	Problem description
[in]	x	Current iterate $x^k$
[in]	y	Lagrange multipliers $y$
[in]	Σ	Penalty weights $\mathrm{\Sigma }$
[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 $\mathrm{\nabla }\psi (x^k)$
	work_x	Dimension n
	work_grad_ψ	Dimension n
	work_n	Dimension n
	work_m	Dimension m

Definition at line 288 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 $\mathrm{\nabla }\psi$ using finite differences.

Parameters

[in]	problem	Problem description
[in]	xₖ	Current iterate $x^k$
[in]	y	Lagrange multipliers $y$
[in]	Σ	Penalty weights $\mathrm{\Sigma }$
[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 $\mathrm{\nabla }\psi (x^k)$
	work_n1	Dimension n
	work_n2	Dimension n
	work_n3	Dimension n
	work_m	Dimension m

Definition at line 338 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