Detailed Description
Parameters to customize the behavior of solvers and directions.
Classes | |
| struct | AndersonAccelParams< Conf > |
| Parameters for the AndersonAccel class. More... | |
| struct | CBFGSParams< Conf > |
| Cautious BFGS update. More... | |
| struct | LBFGSParams< Conf > |
| Parameters for the LBFGS class. More... | |
| struct | SteihaugCGParams< Conf > |
| Parameters for SteihaugCG. More... | |
| struct | AndersonDirectionParams< Conf > |
| Parameters for the AndersonDirection class. More... | |
| struct | LBFGSDirectionParams< Conf > |
| Parameters for the LBFGSDirection class. More... | |
| struct | StructuredLBFGSDirectionParams< Conf > |
| Parameters for the StructuredLBFGSDirection class. More... | |
| struct | StructuredNewtonRegularizationParams< Conf > |
| Parameters for the StructuredNewtonDirection class. More... | |
| struct | StructuredNewtonDirectionParams< Conf > |
| Parameters for the StructuredNewtonDirection class. More... | |
| struct | NewtonTRDirectionParams< Conf > |
| Parameters for the NewtonTRDirection class. More... | |
| struct | FISTAParams< Conf > |
| Tuning parameters for the FISTA algorithm. More... | |
| struct | LipschitzEstimateParams< Conf > |
| Parameters for the estimation of the Lipschitz constant of the gradient of the smooth term of the cost. More... | |
| struct | PANOCOCPParams< Conf > |
| Tuning parameters for the PANOC algorithm. More... | |
| struct | PANOCParams< Conf > |
| Tuning parameters for the PANOC algorithm. More... | |
| struct | PANTRParams< Conf > |
| Tuning parameters for the PANTR algorithm. More... | |
| struct | ZeroFPRParams< Conf > |
| Tuning parameters for the ZeroFPR algorithm. More... | |
| struct | ALMParams< Conf > |
| Parameters for the Augmented Lagrangian solver. More... | |
| struct | LBFGSBParams |
| Tuning parameters for the L-BFGS-B solver LBFGSBSolver. More... | |
Class Documentation
◆ alpaqa::AndersonAccelParams
| struct alpaqa::AndersonAccelParams |
Collaboration diagram for AndersonAccelParams< Conf >:| Class Members | ||
|---|---|---|
| length_t | memory = 10 |
Length of the history to keep (the number of columns in the QR factorization). If this number is greater than the problem dimension, the memory is set to the problem dimension (otherwise the system is underdetermined). |
| real_t | min_div_fac = real_t(1e2) * std::numeric_limits<real_t>::epsilon() | Minimum divisor when solving close to singular systems, scaled by the maximum eigenvalue of R. |
◆ alpaqa::LBFGSParams
| struct alpaqa::LBFGSParams |
Collaboration diagram for LBFGSParams< Conf >:| Class Members | ||
|---|---|---|
| length_t | memory = 10 | Length of the history to keep. |
| real_t | min_div_fac = std::numeric_limits<real_t>::epsilon() |
Reject update if \( y^\top s \le \text{min_div_fac} \cdot s^\top s \). Keeps the inverse Hessian approximation positive definite. |
| real_t | min_abs_s |
Reject update if \( s^\top s \le \text{min_abs_s} \). Keeps the Hessian approximation nonsingular. |
| CBFGSParams< config_t > | cbfgs = {} |
Parameters in the cautious BFGS update condition. \[ \frac{y^\top s}{s^\top s} \ge \epsilon \| g \|^\alpha. \] Disabled by default. |
| bool | force_pos_def = true |
If set to true, the inverse Hessian estimate should remain definite, i.e. a check is performed that rejects the update if \( y^\top s \le \text{min_div_fac} \cdot s^\top s \). If set to false, just try to prevent a singular Hessian by rejecting the update if \( \left| y^\top s \right| \le \text{min_div_fac} \cdot s^\top s \). |
| LBFGSStepSize | stepsize = LBFGSStepSize::BasedOnCurvature |
Scale of the initial inverse Hessian approximation that the rank-one L-BFGS updates are applied to, \( H_0 \). You probably want to keep this as the default.
|
◆ alpaqa::SteihaugCGParams
| struct alpaqa::SteihaugCGParams |
Collaboration diagram for SteihaugCGParams< Conf >:| Class Members | ||
|---|---|---|
| real_t | tol_scale = 1 |
Determines the tolerance for termination of the algorithm. It terminates if the norm of the residual \( r = -g - Hq \) is smaller than the tolerance \[ \mathrm{tolerance} = \min\left( \mathrm{tol\_max},\; \mathrm{tol\_scale}\cdot \|g\|\cdot \min\left(\mathrm{tol\_scale\_root},\; \sqrt{\|g\|}\right) \right) \] |
| real_t | tol_scale_root = real_t(0.5) |
Determines the tolerance for termination of the algorithm. See tol_scale. |
| real_t | tol_max = inf<config_t> |
Determines the tolerance for termination of the algorithm. Prevents the use of huge tolerances if the gradient norm is still large. See tol_scale. |
| real_t | max_iter_factor = 1 | Limit the number of CG iterations to \( \lfloor n \cdot \mathrm{max\_iter\_factor} \rceil \), where \( n \) is the number of free variables of the problem. |
◆ alpaqa::AndersonDirectionParams
| struct alpaqa::AndersonDirectionParams |
◆ alpaqa::LBFGSDirectionParams
| struct alpaqa::LBFGSDirectionParams |
◆ alpaqa::StructuredNewtonRegularizationParams
| struct alpaqa::StructuredNewtonRegularizationParams |
Collaboration diagram for StructuredNewtonRegularizationParams< Conf >:| Class Members | ||
|---|---|---|
| real_t | min_eig = std::cbrt(std::numeric_limits<real_t>::epsilon()) | Minimum eigenvalue of the Hessian, scaled by \( 1 + |\lambda_\mathrm{max}| \), enforced by regularization using a multiple of identity. |
| bool | print_eig = false | Print the minimum and maximum eigenvalue of the Hessian. |
◆ alpaqa::StructuredNewtonDirectionParams
| struct alpaqa::StructuredNewtonDirectionParams |
Collaboration diagram for StructuredNewtonDirectionParams< Conf >:| Class Members | ||
|---|---|---|
| real_t | hessian_vec_factor = 0 |
Set this option to a nonzero value to include the Hessian-vector product \( \nabla^2_{x_\mathcal{J}x_\mathcal{K}}\psi(x) q_\mathcal{K} \) from equation 12b in [4], scaled by this parameter. Set it to zero to leave out that term. |
◆ alpaqa::NewtonTRDirectionParams
| struct alpaqa::NewtonTRDirectionParams |
Collaboration diagram for NewtonTRDirectionParams< Conf >:| Class Members | ||
|---|---|---|
| real_t | hessian_vec_factor = real_t(1) |
The factor in front of the term \( \langle H_{\mathcal{JK}}
d_{\mathcal {K}}, d_{\mathcal{J}} \rangle \) in equation (9) in [1]. Set it to zero to leave out that term (this usually only slightly increases the number of iterations, and eliminates one Hessian-vector product per iteration, improving the overall runtime). |
| bool | finite_diff = false | Use finite differences to compute Hessian-vector products. |
| real_t | finite_diff_stepsize |
Size of the perturbation for the finite differences computation. Multiplied by \( 1+\|x\| \). |
◆ alpaqa::FISTAParams
| struct alpaqa::FISTAParams |
Collaboration diagram for FISTAParams< Conf >:| Class Members | ||
|---|---|---|
| LipschitzEstimateParams< config_t > | Lipschitz | Parameters related to the Lipschitz constant estimate and step size. |
| unsigned | max_iter = 1000 | Maximum number of inner FISTA iterations. |
| nanoseconds | max_time = std::chrono::minutes(5) | Maximum duration. |
| real_t | L_min = real_t(1e-5) | Minimum Lipschitz constant estimate. |
| real_t | L_max = real_t(1e20) | Maximum Lipschitz constant estimate. |
| PANOCStopCrit | stop_crit = PANOCStopCrit::ApproxKKT | What stopping criterion to use. |
| unsigned | max_no_progress = 10 | Maximum number of iterations without any progress before giving up. |
| unsigned | print_interval = 0 |
When to print progress. If set to zero, nothing will be printed. If set to N != 0, progress is printed every N iterations. |
| int | print_precision = std::numeric_limits<real_t>::max_digits10 / 2 | The precision of the floating point values printed by the solver. |
| real_t | quadratic_upperbound_tolerance_factor |
Tolerance factor used in the quadratic upper bound condition that determines the step size. Its goal is to account for numerical errors in the function and gradient evaluations. If you notice that the step size γ becomes very small, you may want to increase this factor. |
| bool | disable_acceleration = false |
Don't compute accelerated steps, fall back to forward-backward splitting. For testing purposes. |
◆ alpaqa::LipschitzEstimateParams
| struct alpaqa::LipschitzEstimateParams |
Collaboration diagram for LipschitzEstimateParams< Conf >:| Class Members | ||
|---|---|---|
| real_t | L_0 = 0 |
Initial estimate of the Lipschitz constant of ∇ψ(x). If set to zero, it will be approximated using finite differences. |
| real_t | ε = real_t(1e-6) | Relative step size for initial finite difference Lipschitz estimate. |
| real_t | δ = real_t(1e-12) | Minimum step size for initial finite difference Lipschitz estimate. |
| real_t | Lγ_factor = real_t(0.95) |
Factor that relates step size γ and Lipschitz constant. Parameter α in Algorithm 2 of [2]. \( 0 < \alpha < 1 \) |
◆ alpaqa::PANOCOCPParams
| struct alpaqa::PANOCOCPParams |
Collaboration diagram for PANOCOCPParams< Conf >:| Class Members | ||
|---|---|---|
| LipschitzEstimateParams< config_t > | Lipschitz | Parameters related to the Lipschitz constant estimate and step size. |
| unsigned | max_iter = 100 | Maximum number of inner PANOC iterations. |
| nanoseconds | max_time = std::chrono::minutes(5) | Maximum duration. |
| real_t | min_linesearch_coefficient = real_t(1. / 256) | Minimum weight factor between Newton step and projected gradient step, line search parameter. |
| real_t | linesearch_strictness_factor = real_t(0.95) |
Parameter β used in the line search (see Algorithm 2 in [2]). \( 0 < \beta < 1 \) |
| real_t | L_min = real_t(1e-5) | Minimum Lipschitz constant estimate. |
| real_t | L_max = real_t(1e20) | Maximum Lipschitz constant estimate. |
| unsigned | L_max_inc = 16 | Maximum number of times to double the Lipschitz constant estimate per iteration. |
| PANOCStopCrit | stop_crit = PANOCStopCrit::ApproxKKT | What stopping criterion to use. |
| unsigned | max_no_progress = 10 | Maximum number of iterations without any progress before giving up. |
| unsigned | gn_interval = 1 | How often to use a Gauss-Newton step. Zero to disable GN entirely. |
| bool | gn_sticky = true | Keep trying to apply a Gauss-Newton step as long as they keep getting accepted with step size one. |
| bool | reset_lbfgs_on_gn_step = false | Flush the L-BFGS buffer when a Gauss-Newton step is accepted. |
| bool | lqr_factor_cholesky = true |
Use a Cholesky factorization for the Riccati recursion. Use LU if set to false. |
| LBFGSParams< config_t > | lbfgs_params | L-BFGS parameters (e.g. memory). |
| unsigned | print_interval = 0 |
When to print progress. If set to zero, nothing will be printed. If set to N != 0, progress is printed every N iterations. |
| int | print_precision = std::numeric_limits<real_t>::max_digits10 / 2 | The precision of the floating point values printed by the solver. |
| real_t | quadratic_upperbound_tolerance_factor |
Tolerance factor used in the quadratic upper bound condition that determines the step size. Its goal is to account for numerical errors in the function and gradient evaluations. If you notice that the step size γ becomes very small, you may want to increase this factor. |
| real_t | linesearch_tolerance_factor |
Tolerance factor used in the line search. Its goal is to account for numerical errors in the function and gradient evaluations. If you notice that accelerated steps are rejected (τ = 0) when getting closer to the solution, you may want to increase this factor. |
| bool | disable_acceleration = false |
Don't compute accelerated steps, fall back to forward-backward splitting. For testing purposes. |
◆ alpaqa::PANOCParams
| struct alpaqa::PANOCParams |
Collaboration diagram for PANOCParams< Conf >:| Class Members | ||
|---|---|---|
| LipschitzEstimateParams< config_t > | Lipschitz | Parameters related to the Lipschitz constant estimate and step size. |
| unsigned | max_iter = 100 | Maximum number of inner PANOC iterations. |
| nanoseconds | max_time = std::chrono::minutes(5) | Maximum duration. |
| real_t | min_linesearch_coefficient = real_t(1. / 256) | Minimum weight factor between Newton step and projected gradient step. |
| bool | force_linesearch = false |
Ignore the line search condition and always accept the accelerated step. (For testing purposes only). |
| real_t | linesearch_strictness_factor = real_t(0.95) |
Parameter β used in the line search (see Algorithm 2 in [2]). \( 0 < \beta < 1 \) |
| real_t | L_min = real_t(1e-5) | Minimum Lipschitz constant estimate. |
| real_t | L_max = real_t(1e20) | Maximum Lipschitz constant estimate. |
| PANOCStopCrit | stop_crit = PANOCStopCrit::ApproxKKT | What stopping criterion to use. |
| unsigned | max_no_progress = 10 | Maximum number of iterations without any progress before giving up. |
| unsigned | print_interval = 0 |
When to print progress. If set to zero, nothing will be printed. If set to N != 0, progress is printed every N iterations. |
| int | print_precision = std::numeric_limits<real_t>::max_digits10 / 2 | The precision of the floating point values printed by the solver. |
| real_t | quadratic_upperbound_tolerance_factor |
Tolerance factor used in the quadratic upper bound condition that determines the step size. Its goal is to account for numerical errors in the function and gradient evaluations. If you notice that the step size γ becomes very small, you may want to increase this factor. |
| real_t | linesearch_tolerance_factor |
Tolerance factor used in the line search. Its goal is to account for numerical errors in the function and gradient evaluations. If you notice that accelerated steps are rejected (τ = 0) when getting closer to the solution, you may want to increase this factor. |
| bool | update_direction_in_candidate = false | Use the candidate point rather than the accepted point to update the quasi-Newton direction. |
| bool | recompute_last_prox_step_after_stepsize_change = false |
If the step size changes, the direction buffer is flushed. The current step will still be used to update the direction, but may still use the old step size. If set to true, the current step will be recomputed with the new step size as well, to match the step in the candidate iterate. |
| bool | eager_gradient_eval = false |
When evaluating ψ(x̂) in a candidate point, always evaluate ∇ψ(x̂) as well. Can be beneficial if computing ∇ψ(x̂) is not much more expensive than computing just ψ(x), and if ∇ψ(x̂) is required in the next iteration (e.g. for the stopping criterion, or when using the NoopDirection). |
◆ alpaqa::PANTRParams
| struct alpaqa::PANTRParams |
Collaboration diagram for PANTRParams< Conf >:| Class Members | ||
|---|---|---|
| LipschitzEstimateParams< config_t > | Lipschitz | Parameters related to the Lipschitz constant estimate and step size. |
| unsigned | max_iter = 100 | Maximum number of inner PANTR iterations. |
| nanoseconds | max_time = std::chrono::minutes(5) | Maximum duration. |
| real_t | L_min = real_t(1e-5) | Minimum Lipschitz constant estimate. |
| real_t | L_max = real_t(1e20) | Maximum Lipschitz constant estimate. |
| PANOCStopCrit | stop_crit = PANOCStopCrit::ApproxKKT | What stopping criterion to use. |
| unsigned | max_no_progress = 10 | Maximum number of iterations without any progress before giving up. |
| unsigned | print_interval = 0 |
When to print progress. If set to zero, nothing will be printed. If set to N != 0, progress is printed every N iterations. |
| int | print_precision = std::numeric_limits<real_t>::max_digits10 / 2 | The precision of the floating point values printed by the solver. |
| real_t | quadratic_upperbound_tolerance_factor |
Tolerance factor used in the quadratic upper bound condition that determines the step size. Its goal is to account for numerical errors in the function and gradient evaluations. If you notice that the step size γ becomes very small, you may want to increase this factor. |
| real_t | TR_tolerance_factor = 10 * std::numeric_limits<real_t>::epsilon() | |
| real_t | ratio_threshold_acceptable = real_t(0.2) | Minimal TR ratio to be accepted (successful). |
| real_t | ratio_threshold_good = real_t(0.8) | Minimal TR ratio to increase radius (very successful). |
| real_t | radius_factor_rejected = real_t(0.35) | TR radius decrease coefficient when unsuccessful. |
| real_t | radius_factor_acceptable = real_t(0.999) | TR radius decrease coefficient when successful. |
| real_t | radius_factor_good = real_t(2.5) | TR radius increase coefficient when very successful. |
| real_t | initial_radius = NaN<config_t> | Initial trust radius. |
| real_t | min_radius = 100 * std::numeric_limits<real_t>::epsilon() | Minimum trust radius. |
| bool | compute_ratio_using_new_stepsize = false | Check the quadratic upperbound and update γ before computing the reduction of the TR step. |
| bool | update_direction_on_prox_step = true | |
| bool | recompute_last_prox_step_after_direction_reset = false | |
| bool | disable_acceleration = false |
Don't compute accelerated steps, fall back to forward-backward splitting. For testing purposes. |
| bool | ratio_approx_fbe_quadratic_model = true |
Compute the trust-region ratio using an approximation of the quadratic model of the FBE, rather than the quadratic model of the subproblem. Specifically, when set to false, the quadratic model used is \[ q(d) = \tfrac12 \inprod{\mathcal R_\gamma(\hat x) d}{d} + \inprod{R_\gamma(\hat x)}{d}. \] When set to true, the quadratic model used is \[ q_\mathrm{approx}(d) = \inv{(1-\alpha)} q(d), \] where \( \alpha = \) LipschitzEstimateParams::Lγ_factor. This is an approximation of the quadratic model of the FBE, \[ q_{\varphi_\gamma}(d) = \tfrac12 \inprod{\mathcal Q_\gamma(\hat x) \mathcal R_\gamma(\hat x) d}{d} + \inprod{\mathcal Q_\gamma(\hat x) R_\gamma(\hat x)}{d}, \] with \( \mathcal Q_\gamma(x) = \Id - \gamma \nabla^2 \psi(x) \). |
◆ alpaqa::ZeroFPRParams
| struct alpaqa::ZeroFPRParams |
Collaboration diagram for ZeroFPRParams< Conf >:| Class Members | ||
|---|---|---|
| LipschitzEstimateParams< config_t > | Lipschitz | Parameters related to the Lipschitz constant estimate and step size. |
| unsigned | max_iter = 100 | Maximum number of inner ZeroFPR iterations. |
| nanoseconds | max_time = std::chrono::minutes(5) | Maximum duration. |
| real_t | min_linesearch_coefficient = real_t(1. / 256) | Minimum weight factor between Newton step and projected gradient step. |
| bool | force_linesearch = false |
Ignore the line search condition and always accept the accelerated step. (For testing purposes only). |
| real_t | linesearch_strictness_factor = real_t(0.95) |
Parameter β used in the line search (see Algorithm 2 in [2]). \( 0 < \beta < 1 \) |
| real_t | L_min = real_t(1e-5) | Minimum Lipschitz constant estimate. |
| real_t | L_max = real_t(1e20) | Maximum Lipschitz constant estimate. |
| PANOCStopCrit | stop_crit = PANOCStopCrit::ApproxKKT | What stopping criterion to use. |
| unsigned | max_no_progress = 10 | Maximum number of iterations without any progress before giving up. |
| unsigned | print_interval = 0 |
When to print progress. If set to zero, nothing will be printed. If set to N != 0, progress is printed every N iterations. |
| int | print_precision = std::numeric_limits<real_t>::max_digits10 / 2 | The precision of the floating point values printed by the solver. |
| real_t | quadratic_upperbound_tolerance_factor |
Tolerance factor used in the quadratic upper bound condition that determines the step size. Its goal is to account for numerical errors in the function and gradient evaluations. If you notice that the step size γ becomes very small, you may want to increase this factor. |
| real_t | linesearch_tolerance_factor |
Tolerance factor used in the line search. Its goal is to account for numerical errors in the function and gradient evaluations. If you notice that accelerated steps are rejected (τ = 0) when getting closer to the solution, you may want to increase this factor. |
| bool | update_direction_in_candidate = false | Use the candidate point rather than the accepted point to update the quasi-Newton direction. |
| bool | recompute_last_prox_step_after_stepsize_change = false |
If the step size changes, the direction buffer is flushed. The current step will still be used to update the direction, but may still use the old step size. If set to true, the current step will be recomputed with the new step size as well, to match the step in the candidate iterate. |
| bool | update_direction_from_prox_step = false | Update the direction between current forward-backward point and the candidate iterate instead of between the current iterate and the candidate iterate. |
◆ alpaqa::ALMParams
| struct alpaqa::ALMParams |
Collaboration diagram for ALMParams< Conf >:| Class Members | ||
|---|---|---|
| real_t | tolerance = real_t(1e-5) | Primal tolerance (used for stopping criterion of inner solver). |
| real_t | dual_tolerance = real_t(1e-5) | Dual tolerance (constraint violation and complementarity). |
| real_t | penalty_update_factor = 10 | Factor used in updating the penalty parameters. |
| real_t | initial_penalty = 1 |
Initial penalty parameter. When set to zero (which is the default), it is computed automatically, based on the constraint violation in the starting point and the parameter initial_penalty_factor. |
| real_t | initial_penalty_factor = 20 |
Initial penalty parameter factor. Active if initial_penalty is set to zero. |
| real_t | initial_tolerance = 1 | Initial primal tolerance. |
| real_t | tolerance_update_factor = real_t(1e-1) | Update factor for primal tolerance. |
| real_t | rel_penalty_increase_threshold = real_t(0.1) | Error tolerance for penalty increase. |
| real_t | max_multiplier = real_t(1e9) | Lagrange multiplier bound. |
| real_t | max_penalty = real_t(1e9) | Maximum penalty factor. |
| real_t | min_penalty = real_t(1e-9) | Minimum penalty factor (used during initialization). |
| unsigned int | max_iter = 100 | Maximum number of outer ALM iterations. |
| nanoseconds | max_time = std::chrono::minutes(5) | Maximum duration. |
| unsigned | print_interval = 0 |
When to print progress. If set to zero, nothing will be printed. If set to N != 0, progress is printed every N iterations. |
| int | print_precision = std::numeric_limits<real_t>::max_digits10 / 2 | The precision of the floating point values printed by the solver. |
| bool | single_penalty_factor = false | Use one penalty factor for all m constraints. |
◆ alpaqa::lbfgsb::LBFGSBParams
| struct alpaqa::lbfgsb::LBFGSBParams |
Collaboration diagram for LBFGSBParams:| Class Members | ||
|---|---|---|
| unsigned | memory = 10 | |
| unsigned | max_iter = 1000 | |
| nanoseconds | max_time = std::chrono::minutes(5) | |
| PANOCStopCrit | stop_crit = PANOCStopCrit::ProjGradUnitNorm | |
| int | print = -1 | |
| unsigned | print_interval = 0 | |
| int | print_precision = std::numeric_limits<real_t>::max_digits10 / 2 | |
