alpaqa::detail Namespace Reference

Functions
void	project_y (rvec y, crvec z_lb, crvec z_ub, real_t M)
void	update_penalty_weights (const ALMParams &params, real_t Δ, bool first_iter, rvec e, rvec old_e, real_t norm_e, real_t old_norm_e, crvec Σ_old, rvec Σ)
void	initialize_penalty (const Problem &p, const ALMParams &params, crvec x0, rvec Σ)
void	apply_preconditioning (const Problem &problem, Problem &prec_problem, crvec x, real_t &prec_f, vec &prec_g)
real_t	calc_ψ_ŷ (const Problem &p, crvec x, crvec y, crvec Σ, rvec ŷ)
	Calculate both ψ(x) and the vector ŷ that can later be used to compute ∇ψ. More...
void	calc_grad_ψ_from_ŷ (const Problem &p, crvec x, crvec ŷ, rvec grad_ψ, rvec work_n)
	Calculate ∇ψ(x) using ŷ. More...
real_t	calc_ψ_grad_ψ (const Problem &p, crvec x, crvec y, crvec Σ, rvec grad_ψ, rvec work_n, rvec work_m)
	Calculate both ψ(x) and its gradient ∇ψ(x). More...
void	calc_grad_ψ (const Problem &p, crvec x, crvec y, crvec Σ, rvec grad_ψ, rvec work_n, rvec work_m)
	Calculate the gradient ∇ψ(x). More...
void	calc_err_z (const Problem &p, crvec x̂, crvec y, crvec Σ, rvec err_z)
	Calculate the error between ẑ and g(x). More...
auto	projected_gradient_step (const Box &C, real_t γ, crvec x, crvec grad_ψ)
	Projected gradient step. More...
void	calc_x̂ (const Problem &prob, real_t γ, crvec x, crvec grad_ψ, rvec x̂, rvec p)
bool	stop_crit_requires_grad_̂ψₖ (PANOCStopCrit crit)
real_t	calc_error_stop_crit (const Box &C, PANOCStopCrit crit, crvec pₖ, real_t γ, crvec xₖ, crvec x̂ₖ, crvec ŷₖ, crvec grad_ψₖ, crvec grad_̂ψₖ)
	Compute the ε from the stopping criterion, see PANOCStopCrit. More...
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: More...
template<class ParamsT , class DurationT >
SolverStatus	check_all_stop_conditions (const ParamsT &params, DurationT time_elapsed, unsigned iteration, const AtomicStopSignal &stop_signal, real_t ε, 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) More...
void	calc_augmented_lagrangian_hessian (const Problem &problem, crvec xₖ, crvec ŷxₖ, crvec y, crvec Σ, rvec g, mat &H, rvec work_n)
	Compute the Hessian matrix of the augmented Lagrangian function. More...
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. More...
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, real_t &ψ, 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. More...
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. More...
template<class ObjFunT , class ObjGradFunT >
real_t	initial_lipschitz_estimate (const ObjFunT &ψ, const ObjGradFunT &grad_ψ, crvec xₖ, real_t ε, real_t δ, real_t L_min, real_t L_max, real_t &ψₖ, rvec grad_ψₖ, vec_allocator &alloc)
	Estimate the Lipschitz constant of the gradient $\mathrm{\nabla }\psi$ using finite differences. More...
void	calc_x̂ (real_t γ, crvec x, const Box &C, crvec grad_ψ, rvec x̂, rvec p)
template<class ObjFunT >
real_t	descent_lemma (const ObjFunT &ψ, const Box &C, real_t rounding_tolerance, real_t L_max, crvec xₖ, real_t ψₖ, crvec grad_ψₖ, rvec x̂ₖ, rvec pₖ, 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: More...
void	print_progress (unsigned k, real_t ψₖ, crvec grad_ψₖ, real_t pₖᵀpₖ, real_t γₖ, real_t εₖ)

Function Documentation

project_y()

void alpaqa::detail::project_y ( rvec  y, crvec  z_lb, crvec  z_ub, real_t  M  )

inline

Definition at line 8 of file alm-helpers.hpp.

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update_penalty_weights()

void alpaqa::detail::update_penalty_weights ( const ALMParams &  params, real_t  Δ, bool  first_iter, rvec  e, rvec  old_e, real_t  norm_e, real_t  old_norm_e, crvec  Σ_old, rvec  Σ  )

inline

Definition at line 25 of file alm-helpers.hpp.

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initialize_penalty()

void alpaqa::detail::initialize_penalty ( const Problem &  p, const ALMParams &  params, crvec  x0, rvec  Σ  )

inline

Definition at line 53 of file alm-helpers.hpp.

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apply_preconditioning()

void alpaqa::detail::apply_preconditioning ( const Problem &  problem, Problem &  prec_problem, crvec  x, real_t &  prec_f, vec &  prec_g  )

inline

Definition at line 66 of file alm-helpers.hpp.

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calc_ψ_ŷ()

real_t alpaqa::detail::calc_ψ_ŷ ( const Problem &  p, crvec  x, crvec  y, crvec  Σ, rvec  ŷ  )

inline

Calculate both ψ(x) and the vector ŷ that can later be used to compute ∇ψ.

$$\psi (x^k)=f(x^k)+\frac{1}{2}{\text{dist}}_{\mathrm{\Sigma }}^2(g(x^k)+{\mathrm{\Sigma }}^{-1}y,D)$$

$$\hat{y}$$

Parameters

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

Definition at line 16 of file panoc-helpers.hpp.

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calc_grad_ψ_from_ŷ()

void alpaqa::detail::calc_grad_ψ_from_ŷ ( const Problem &  p, crvec  x, crvec  ŷ, rvec  grad_ψ, rvec  work_n  )

inline

Calculate ∇ψ(x) using ŷ.

Parameters

[in]	p	Problem description
[in]	x	Decision variable $x$
[in]	ŷ	$\hat{y}$
[out]	grad_ψ	$\mathrm{\nabla }\psi (x)$
	work_n	Dimension n

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

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calc_ψ_grad_ψ()

real_t alpaqa::detail::calc_ψ_grad_ψ ( const Problem &  p, crvec  x, crvec  y, crvec  Σ, rvec  grad_ψ, rvec  work_n, rvec  work_m  )

inline

Calculate both ψ(x) and its gradient ∇ψ(x).

$$\psi (x^k)=f(x^k)+\frac{1}{2}{\text{dist}}_{\mathrm{\Sigma }}^2(g(x^k)+{\mathrm{\Sigma }}^{-1}y,D)$$

$$\mathrm{\nabla }\psi (x)=\mathrm{\nabla }f(x)+\mathrm{\nabla }g(x)\hat{y}(x)$$

Parameters

[in]	p	Problem description
[in]	x	Decision variable $x$
[in]	y	Lagrange multipliers $y$
[in]	Σ	Penalty weights $\mathrm{\Sigma }$
[out]	grad_ψ	$\mathrm{\nabla }\psi (x)$
	work_n	Dimension n
	work_m	Dimension m

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

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calc_grad_ψ()

void alpaqa::detail::calc_grad_ψ ( const Problem &  p, crvec  x, crvec  y, crvec  Σ, rvec  grad_ψ, rvec  work_n, rvec  work_m  )

inline

Calculate the gradient ∇ψ(x).

$$\mathrm{\nabla }\psi (x)=\mathrm{\nabla }f(x)+\mathrm{\nabla }g(x)\hat{y}(x)$$

Parameters

[in]	p	Problem description
[in]	x	Decision variable $x$
[in]	y	Lagrange multipliers $y$
[in]	Σ	Penalty weights $\mathrm{\Sigma }$
[out]	grad_ψ	$\mathrm{\nabla }\psi (x)$
	work_n	Dimension n
	work_m	Dimension m

Definition at line 79 of file panoc-helpers.hpp.

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calc_err_z()

void alpaqa::detail::calc_err_z ( const Problem &  p, crvec  x̂, crvec  y, crvec  Σ, rvec  err_z  )

inline

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 107 of file panoc-helpers.hpp.

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projected_gradient_step()

auto alpaqa::detail::projected_gradient_step ( const Box &  C, real_t  γ, crvec  x, crvec  grad_ψ  )

inline

Projected gradient step.

$$\begin{array}{rl}{\hat{x}}^k& =T_{{\gamma }^k}\left(x^k\right)\\ & ={\mathrm{\Pi }}_C(x^k-{\gamma }^k\mathrm{\nabla }\psi (x^k))\\ p^k& ={\hat{x}}^k-x^k\end{array}$$

Parameters

[in]	C	Set to project onto
[in]	γ	Step size
[in]	x	Decision variable $x$
[in]	grad_ψ	$\mathrm{\nabla }\psi (x^k)$

Definition at line 131 of file panoc-helpers.hpp.

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calc_x̂() [1/2]

void alpaqa::detail::calc_x̂ ( const Problem &  prob, real_t  γ, crvec  x, crvec  grad_ψ, rvec  x̂, rvec  p  )

inline

Parameters

[in]	prob	Problem description
[in]	γ	Step size
[in]	x	Decision variable $x$
[in]	grad_ψ	$\mathrm{\nabla }\psi (x^k)$
[out]	x̂	${\hat{x}}^k=T_{{\gamma }^k}(x^k)$
[out]	p	${\hat{x}}^k-x^k$

Definition at line 142 of file panoc-helpers.hpp.

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stop_crit_requires_grad_̂ψₖ()

bool alpaqa::detail::stop_crit_requires_grad_̂ψₖ ( PANOCStopCrit  crit )

inline

Definition at line 153 of file panoc-helpers.hpp.

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calc_error_stop_crit()

real_t alpaqa::detail::calc_error_stop_crit ( const Box &  C, PANOCStopCrit  crit, crvec  pₖ, real_t  γ, crvec  xₖ, crvec  x̂ₖ, crvec  ŷₖ, crvec  grad_ψₖ, crvec  grad_̂ψₖ  )

inline

Compute the ε from the stopping criterion, see PANOCStopCrit.

Parameters

[in]	C	Box constraints on x
[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 ${\hat{x}}^k$

Definition at line 169 of file panoc-helpers.hpp.

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descent_lemma() [1/2]

real_t alpaqa::detail::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  )

inline

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 $\hat{y}(x^k)$
[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 242 of file panoc-helpers.hpp.

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check_all_stop_conditions()

SolverStatus alpaqa::detail::check_all_stop_conditions ( const ParamsT &  params, DurationT  time_elapsed, unsigned  iteration, const AtomicStopSignal &  stop_signal, real_t  ε, real_t  εₖ, unsigned  no_progress  )

inline

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]	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]	ε	Desired primal tolerance
[in]	εₖ	Tolerance of the current iterate
[in]	no_progress	The number of successive iterations no progress was made

Definition at line 307 of file panoc-helpers.hpp.

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calc_augmented_lagrangian_hessian()

void alpaqa::detail::calc_augmented_lagrangian_hessian ( const Problem &  problem, crvec  xₖ, crvec  ŷxₖ, crvec  y, crvec  Σ, rvec  g, mat &  H, rvec  work_n  )

inline

Compute the Hessian matrix of the augmented Lagrangian function.

$${\mathrm{\nabla }}_{xx}^2{L}_{\mathrm{\Sigma }}(x,y)={\mathrm{\nabla }}_{xx}^{2}L(x,y){|}_{(x,\hat{y}(x,y))}+\sum _{i\in \mathcal{I}}{\mathrm{\Sigma }}_i\mathrm{\nabla }{g}_i(x)\mathrm{\nabla }{g}_i(x{)}^{\mathrm{\top }}$$

Parameters

[in]	problem	Problem description
[in]	xₖ	Current iterate $x^k$
[in]	ŷxₖ	Intermediate vector $\hat{y}(x^k)$
[in]	y	Lagrange multipliers $y$
[in]	Σ	Penalty weights $\mathrm{\Sigma }$
[out]	g	The constraint values $g(x^k)$
[out]	H	Hessian matrix $H(x,y)$
	work_n	Dimension n

Definition at line 342 of file panoc-helpers.hpp.

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calc_augmented_lagrangian_hessian_prod_fd()

void alpaqa::detail::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  )

inline

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 379 of file panoc-helpers.hpp.

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initial_lipschitz_estimate() [1/3]

real_t alpaqa::detail::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, real_t &  ψ, rvec  grad_ψ, rvec  work_n1, rvec  work_n2, rvec  work_n3, rvec  work_m  )

inline

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]	ψ	$\psi (x^k)$
[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 412 of file panoc-helpers.hpp.

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initial_lipschitz_estimate() [2/3]

real_t alpaqa::detail::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  )

inline

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 459 of file panoc-helpers.hpp.

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initial_lipschitz_estimate() [3/3]

real_t alpaqa::detail::initial_lipschitz_estimate	(	const ObjFunT &	ψ,
		const ObjGradFunT &	grad_ψ,
		crvec	xₖ,
		real_t	ε,
		real_t	δ,
		real_t	L_min,
		real_t	L_max,
		real_t &	ψₖ,
		rvec	grad_ψₖ,
		vec_allocator &	alloc
	)

Estimate the Lipschitz constant of the gradient $\mathrm{\nabla }\psi$ using finite differences.

Parameters

[in]	ψ	Objective
[in]	grad_ψ	Gradient of
[in]	xₖ	Current iterate $x^k$
[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]	ψₖ	$\psi (x^k)$
[out]	grad_ψₖ	Gradient $\mathrm{\nabla }\psi (x^k)$
[in]	alloc

Definition at line 20 of file standalone/panoc.hpp.

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calc_x̂() [2/2]

void alpaqa::detail::calc_x̂ ( real_t  γ, crvec  x, const Box &  C, crvec  grad_ψ, rvec  x̂, rvec  p  )

inline

Parameters

[in]	γ	Step size
[in]	x	Decision variable $x$
[in]	C	Box constraints $C$
[in]	grad_ψ	$\mathrm{\nabla }\psi (x^k)$
[out]	x̂	${\hat{x}}^k=T_{{\gamma }^k}(x^k)$
[out]	p	${\hat{x}}^k-x^k$

Definition at line 58 of file standalone/panoc.hpp.

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descent_lemma() [2/2]

real_t alpaqa::detail::descent_lemma	(	const ObjFunT &	ψ,
		const Box &	C,
		real_t	rounding_tolerance,
		real_t	L_max,
		crvec	xₖ,
		real_t	ψₖ,
		crvec	grad_ψₖ,
		rvec	x̂ₖ,
		rvec	pₖ,
		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:

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

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]	ψ	Objective.
[in]	C	Box constraints.
[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 $\mathrm{\nabla }\psi (x^k)$
[out]	x̂ₖ	Projected gradient iterate ${\hat{x}}^k$
[out]	pₖ	Projected gradient step $p^k$
[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 82 of file standalone/panoc.hpp.

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print_progress()

void alpaqa::detail::print_progress ( unsigned  k, real_t  ψₖ, crvec  grad_ψₖ, real_t  pₖᵀpₖ, real_t  γₖ, real_t  εₖ  )

inline

Definition at line 139 of file standalone/panoc.hpp.

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