Augmented Lagrangian solver#

group grp_ALMSolver

Augmented Lagrangian Method solver (ALM).

template<class InnerSolverT> class ALMSolver

#include <alpaqa/outer/alm.hpp>

Augmented Lagrangian Method solver.

Public Types

using Params = ALMParams<config_t>

using InnerSolver = InnerSolverT

using Problem = typename InnerSolver::Problem

Public Functions

inline ALMSolver(Params params, InnerSolver &&inner_solver)

inline ALMSolver(Params params, const InnerSolver &inner_solver)

Stats operator()(const Problem &problem, rvec x, rvec y, std::optional<rvec> Σ = std::nullopt)

template<class P> inline Stats operator()(const P &problem, rvec x, rvec y, std::optional<rvec> Σ = std::nullopt)

inline std::string get_name() const

inline void stop()

Abort the computation and return the result so far.

Can be called from other threads or signal handlers.

inline const Params &get_params() const

Public Members

InnerSolver inner_solver

std::ostream *os = &std::cout

struct Stats

#include <alpaqa/outer/alm.hpp>

Public Members

unsigned outer_iterations = 0

Total number of outer ALM iterations (i.e.

the number of times that the inner solver was invoked).

std::chrono::nanoseconds elapsed_time = {}: Total elapsed time.

unsigned initial_penalty_reduced = 0

The number of times that the initial penalty factor was reduced by ALMParams::initial_penalty_lower and that the initial tolerance was increased by ALMParams::initial_tolerance_increase because the inner solver failed to converge in the first ALM iteration.

If this number is greater than zero, consider lowering the initial penalty factor ALMParams::initial_penalty or ALMParams::initial_penalty_factor or increasing the initial tolerance ALMParams::initial_tolerance (or both).

unsigned penalty_reduced = 0

The number of times that the penalty update factor ALMParams::penalty_update_factor was reduced, that the tolerance update factor ALMParams::tolerance_update_factor was increased, and that an ALM iteration had to be restarted with a lower penalty factor and a higher tolerance because the inner solver failed to converge (not applicable in the first ALM iteration).

If this number is greater than zero, consider lowerering the penalty update factor ALMParams::penalty_update_factor or increasing the tolerance update factor (or both). Lowering the initial penalty factor could help as well.

unsigned inner_convergence_failures = 0: The total number of times that the inner solver failed to converge.

real_t ε = inf<config_t>: Final primal tolerance that was reached, depends on the stopping criterion used by the inner solver, see for example PANOCStopCrit.

real_t δ = inf<config_t>

Final dual tolerance or constraint violation that was reached:

\[ \delta = \| \Pi_D\left(g(x^k) + \Sigma^{-1}y\right) \|_\infty \]

real_t norm_penalty = 0: 2-norm of the final penalty factors \( \| \Sigma \|_2 \).

SolverStatus status = SolverStatus::Busy

Whether the solver converged or not.