arc_control_type structure#

    struct arc_control_type{T}
      f_indexing::Bool
      error::Int32
      out::Int32
      print_level::Int32
      start_print::Int32
      stop_print::Int32
      print_gap::Int32
      maxit::Int32
      alive_unit::Int32
      alive_file::NTuple{31,Cchar}
      non_monotone::Int32
      model::Int32
      norm::Int32
      semi_bandwidth::Int32
      lbfgs_vectors::Int32
      max_dxg::Int32
      icfs_vectors::Int32
      mi28_lsize::Int32
      mi28_rsize::Int32
      advanced_start::Int32
      stop_g_absolute::T
      stop_g_relative::T
      stop_s::T
      initial_weight::T
      minimum_weight::T
      reduce_gap::T
      tiny_gap::T
      large_root::T
      eta_successful::T
      eta_very_successful::T
      eta_too_successful::T
      weight_decrease_min::T
      weight_decrease::T
      weight_increase::T
      weight_increase_max::T
      obj_unbounded::T
      cpu_time_limit::T
      clock_time_limit::T
      hessian_available::Bool
      subproblem_direct::Bool
      renormalize_weight::Bool
      quadratic_ratio_test::Bool
      space_critical::Bool
      deallocate_error_fatal::Bool
      prefix::NTuple{31,Cchar}
      rqs_control::rqs_control_type{T}
      glrt_control::glrt_control_type{T}
      dps_control::dps_control_type{T}
      psls_control::psls_control_type{T}
      lms_control::lms_control_type{T}
      lms_control_prec::lms_control_type{T}
      sha_control::sha_control_type

detailed documentation#

control derived type as a Julia structure

components#

Bool f_indexing

use C or Fortran sparse matrix indexing

Int32 error

error and warning diagnostics occur on stream error

Int32 out

general output occurs on stream out

Int32 print_level

the level of output required.

  • \(\leq\) 0 gives no output,

  • = 1 gives a one-line summary for every iteration,

  • = 2 gives a summary of the inner iteration for each iteration,

  • \(\geq\) 3 gives increasingly verbose (debugging) output

Int32 start_print

any printing will start on this iteration

Int32 stop_print

any printing will stop on this iteration

Int32 print_gap

the number of iterations between printing

Int32 maxit

the maximum number of iterations performed

Int32 alive_unit

removal of the file alive_file from unit alive_unit terminates execution

char alive_file[31]

see alive_unit

Int32 non_monotone

the descent strategy used.

Possible values are

  • <= 0 a monotone strategy is used.

  • anything else, a non-monotone strategy with history length .non_monotine is used.

Int32 model

the model used.

Possible values are

  • 0 dynamic (not yet implemented)

  • 1 first-order (no Hessian)

  • 2 second-order (exact Hessian)

  • 3 barely second-order (identity Hessian)

  • 4 secant second-order (limited-memory BFGS, with .lbfgs_vectors history) (not yet implemented)

  • 5 secant second-order (limited-memory SR1, with .lbfgs_vectors history) (not yet implemented)

Int32 norm

the regularization norm used.

The norm is defined via \(\|v\|^2 = v^T P v\), and will define the preconditioner used for iterative methods. Possible values for \(P\) are

  • -3 users own preconditioner

  • -2 \(P =\) limited-memory BFGS matrix (with .lbfgs_vectors history)

  • -1 identity (= Euclidan two-norm)

  • 0 automatic (not yet implemented)

  • 1 diagonal, \(P =\) diag( max( Hessian, .min_diagonal ) )

  • 2 banded, \(P =\) band( Hessian ) with semi-bandwidth .semi_bandwidth

  • 3 re-ordered band, P=band(order(A)) with semi-bandwidth .semi_bandwidth

  • 4 full factorization, \(P =\) Hessian, Schnabel-Eskow modification

  • 5 full factorization, \(P =\) Hessian, GMPS modification (not yet implemented)

  • 6 incomplete factorization of Hessian, Lin-More’

  • 7 incomplete factorization of Hessian, HSL_MI28

  • 8 incomplete factorization of Hessian, Munskgaard (not yet implemented)

  • 9 expanding band of Hessian (not yet implemented)

  • 10 diagonalizing norm from GALAHAD_DPS (subproblem_direct only)

Int32 semi_bandwidth

specify the semi-bandwidth of the band matrix P if required

Int32 lbfgs_vectors

number of vectors used by the L-BFGS matrix P if required

Int32 max_dxg

number of vectors used by the sparsity-based secant Hessian if required

Int32 icfs_vectors

number of vectors used by the Lin-More’ incomplete factorization matrix P if required

Int32 mi28_lsize

the maximum number of fill entries within each column of the incomplete factor L computed by HSL_MI28. In general, increasing .mi28_lsize improve the quality of the preconditioner but increases the time to compute and then apply the preconditioner. Values less than 0 are treated as 0

Int32 mi28_rsize

the maximum number of entries within each column of the strictly lower triangular matrix \(R\) used in the computation of the preconditioner by HSL_MI28. Rank-1 arrays of size .mi28_rsize \* n are allocated internally to hold \(R\). Thus the amount of memory used, as well as the amount of work involved in computing the preconditioner, depends on .mi28_rsize. Setting .mi28_rsize > 0 generally leads to a higher quality preconditioner than using .mi28_rsize = 0, and choosing .mi28_rsize >= .mi28_lsize is generally recommended

Int32 advanced_start

try to pick a good initial regularization weight using .advanced_start iterates of a variant on the strategy of Sartenaer SISC 18(6) 1990:1788-1803

T stop_g_absolute

overall convergence tolerances. The iteration will terminate when the norm of the gradient of the objective function is smaller than MAX( .stop_g_absolute, .stop_g_relative * norm of the initial gradient ) or if the step is less than .stop_s

T stop_g_relative

see stop_g_absolute

T stop_s

see stop_g_absolute

T initial_weight

Initial value for the regularisation weight (-ve => 1/||g_0||)

T minimum_weight

minimum permitted regularisation weight

T reduce_gap

expert parameters as suggested in Gould, Porcelli & Toint, “Updating the regularization parameter in the adaptive cubic regularization algorithm” RAL-TR-2011-007, Rutherford Appleton Laboratory, England (2011), http://epubs.stfc.ac.uk/bitstream/6181/RAL-TR-2011-007.pdf (these are denoted beta, epsilon_chi and alpha_max in the paper)

T tiny_gap

see reduce_gap

T large_root

see reduce_gap

T eta_successful

a potential iterate will only be accepted if the actual decrease f - f(x_new) is larger than .eta_successful times that predicted by a quadratic model of the decrease. The regularization weight will be decreased if this relative decrease is greater than .eta_very_successful but smaller than .eta_too_successful (the first is eta in Gould, Porcell and Toint, 2011)

T eta_very_successful

see eta_successful

T eta_too_successful

see eta_successful

T weight_decrease_min

on very successful iterations, the regularization weight will be reduced by the factor .weight_decrease but no more than .weight_decrease_min while if the iteration is unsuccessful, the weight will be increased by a factor .weight_increase but no more than .weight_increase_max (these are delta_1, delta_2, delta3 and delta_max in Gould, Porcelli and Toint, 2011)

T weight_decrease

see weight_decrease_min

T weight_increase

see weight_decrease_min

T weight_increase_max

see weight_decrease_min

T obj_unbounded

the smallest value the onjective function may take before the problem is marked as unbounded

T cpu_time_limit

the maximum CPU time allowed (-ve means infinite)

T clock_time_limit

the maximum elapsed clock time allowed (-ve means infinite)

Bool hessian_available

is the Hessian matrix of second derivatives available or is access only via matrix-vector products?

Bool subproblem_direct

use a direct (factorization) or (preconditioned) iterative method to find the search direction

Bool renormalize_weight

should the weight be renormalized to account for a change in preconditioner?

Bool quadratic_ratio_test

should the test for acceptance involve the quadratic model or the cubic?

Bool space_critical

if .space_critical true, every effort will be made to use as little space as possible. This may result in longer computation time

Bool deallocate_error_fatal

if .deallocate_error_fatal is true, any array/pointer deallocation error will terminate execution. Otherwise, computation will continue

NTuple{31,Cchar} prefix

all output lines will be prefixed by .prefix(2:LEN(TRIM(.prefix))-1) where .prefix contains the required string enclosed in quotes, e.g. “string” or ‘string’

struct rqs_control_type rqs_control

control parameters for RQS

struct glrt_control_type glrt_control

control parameters for GLRT

struct dps_control_type dps_control

control parameters for DPS

struct psls_control_type psls_control

control parameters for PSLS

struct lms_control_type lms_control

control parameters for LMS

struct lms_control_type lms_control_prec

control parameters for LMS used for preconditioning

struct sha_control_type sha_control

control parameters for SHA