Accelerators#

group grp_Accelerators

Computing accelerated directions, such as L-BFGS.

template<Config Conf = DefaultConfig> class AndersonAccel#

#include <alpaqa/accelerators/anderson.hpp>

Anderson Acceleration.

Algorithm for accelerating fixed-point iterations for finding fixed points of a function \( g \), i.e. \( g(x^\star) = x^\star \), or equivalently, roots of the residual \( r(x) \triangleq g(x) - x \).

Public Types

using Params = AndersonAccelParams<config_t>#

Public Functions

AndersonAccel() = default#

inline AndersonAccel(Params params)#

Parameters:: params – Parameters.

inline AndersonAccel(Params params, length_t n)#

Parameters:

params – Parameters.
n – Problem dimension (size of the vectors).

inline void resize(length_t n)#

Change the problem dimension.

Flushes the history.

Parameters:: n – Problem dimension (size of the vectors).

inline void initialize(crvec g_0, crvec r_0)#: Call this function on the first iteration to initialize the accelerator.

inline void compute(crvec gₖ, crvec rₖ, rvec xₖ_aa)#: Compute the accelerated iterate \( x^k_\text{AA} \), given the function value at the current iterate \( g^k = g(x^k) \) and the corresponding residual \( r^k = g^k - x^k \).

inline void compute(crvec gₖ, vec &&rₖ, rvec xₖ_aa)#: Compute the accelerated iterate \( x^k_\text{AA} \), given the function value at the current iterate \( g^k = g(x^k) \) and the corresponding residual \( r^k = g^k - x^k \).

inline void reset()#: Reset the accelerator (but keep the last function value and residual, so calling initialize is not necessary).

inline length_t n() const#: Get the problem dimension.

inline length_t history() const#: Get the maximum number of stored columns.

inline length_t current_history() const#: Get the number of columns currently stored in the buffer.

inline const Params &get_params() const#: Get the parameters.

inline std::string get_name() const#

inline void scale_R(real_t scal)#: Scale the factorization.

inline const LimitedMemoryQR<config_t> &get_QR() const#: For testing purposes.

template<Config Conf = DefaultConfig> class LBFGS#

#include <alpaqa/accelerators/lbfgs.hpp>

Limited memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm.

Public Types

enum class Sign#

The sign of the vectors \( p \) passed to the update method.

Values:

enumerator Positive#: \( p \sim \nabla \psi(x) \)

enumerator Negative#: \( p \sim -\nabla \psi(x) \)

using Params = LBFGSParams<config_t>#

Public Functions

LBFGS() = default#

inline LBFGS(Params params)#

inline LBFGS(Params params, length_t n)#

bool update_sy(crvec s, crvec y, real_t pₙₑₓₜᵀpₙₑₓₜ, bool forced = false)#: Update the inverse Hessian approximation using the new vectors sₖ = xₙₑₓₜ - xₖ and yₖ = pₙₑₓₜ - pₖ.

bool update_sy_impl(const auto &s, const auto &y, real_t pₙₑₓₜᵀpₙₑₓₜ, bool forced = false)#