File numerics/src/tools/NMS.h

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Non-Monotone Stabilisation Scheme for path search.

Main reference for this implementation: Linear Algebra Enhancements to the PATH Solver, by Li, Ferris and Munson

Functions

int NMS(NMS_data *data_NMS, void *data, functions_LSA *functions, double *z, double *z_N, int force_watchdog_step, int force_d_step_merit_check, double check_ratio)

Non-Monotone Stabilisation scheme.

Parameters

  • data_NMS – the NMS data

  • data – opaque data for the computation of the problem

  • functions – struct holding the functions for the computation of F, the merit function

  • z – [inout] on input, current iterate of the solution; on output, the new iterate

  • z_N – proposed iterate for the solution

  • force_watchdog_step – force a watchdog step if the path search failed!

  • force_d_step_merit_check – accept the point at d_step even if the merit function increases. Usually this means that the normal map norm decreases a lot

  • check_ratio – if the norm of the normal map decreases, allow the merit to increase by that much

Returns

0 if succeeded, 1 if failed

NMS_data *create_NMS_data(unsigned size, int matrix_type, int *iparam, double *dparam)

create (allocate) a NMS_data struct and do some allocation work

Parameters

  • size – size of the problem

  • matrix_type – type of the NumericsMatrix used: dense, sparse, …

  • iparam – vector of integer parameters from a SolverOptions struct

  • dparam – vector of double parameters from a SolverOptions struct

Returns

the allocated struct

void free_NMS_data(NMS_data *data)

free a NMS_data struct

Parameters

data – the structure to free

static inline double *NMS_get_F(double *workspace, int n)

Get the F vector from the workspace data.

Parameters

  • workspace – the workspace holding the allocated vectors

  • n – size of vector

Returns

the F vector

static inline double *NMS_get_F_merit(double *workspace, int n)

Get the F_merit vector from the workspace data.

Parameters

  • workspace – the workspace holding the allocated vectors

  • n – size of vector

Returns

the F_merit vector

static inline double *NMS_get_JacTheta_F_merit(double *workspace, int n)

Get the JacTheta_F_merit vector from the workspace data.

Parameters

  • workspace – the workspace holding the allocated vectors

  • n – size of vector

Returns

the JacTheta_F_merit vector

static inline double *NMS_get_dir(double *workspace, int n)

Get the vector for the descent direction from the workspace data.

Parameters

  • workspace – the workspace holding the allocated vectors

  • n – size of vector

Returns

the vector for the descent direction

static inline double *NMS_get_generic_workV(double *workspace, int n)

Get the workV vector from the workspace data.

Parameters

  • workspace – the workspace holding the allocated vectors

  • n – size of vector

Returns

the workV vector

static inline double *NMS_checkpoint_0(NMS_data *data_NMS, unsigned n)

Get the z_c(0) from the workspace data.

Parameters

  • data_NMS – the data for the NMS scheme

  • n – size of vector

Returns

the checkpoint z_c(0)

static inline double *NMS_checkpoint_T(NMS_data *data_NMS, unsigned n)

Get the z_c(T) from the workspace data.

Parameters

  • data_NMS – the data for the NMS scheme

  • n – size of vector

Returns

the checkpoint z_c(T)

static inline double *NMS_bestpoint(NMS_data *data_NMS, unsigned n)

Get the bestpoint z_b from the workspace data.

Parameters

  • data_NMS – the data for the NMS scheme

  • n – size of vector

Returns

the bestpoint z_b

static inline int check_nmd_criterion(double theta_iter, double ref_merit, double sigma, double dotprod)

check the non-monotone descent criterion

Parameters

  • theta_iter – current theta value

  • ref_merit – the reference value for the merit function

  • sigma – the \(\sigma\) parameter

  • dotprod – the value of the inner product between JacThetaF_merit and the descent direction

Returns

0 if the step is accepted, 1 otherwise

struct path_record
#include <>

Save the path generated by the algorithm.

Public Members

int *final_basis

last basis before exit

int *basis_change

record of the changes in the basis (leaving variable and index) use to reconstruct the path.

it is used as a circular buffer

int circular_indx

index to mark the current position in the buffer

struct NMS_data
#include <>

Data for the Non-Monotone Stabilisation scheme.

Public Members

unsigned size

dimension of the space

int watchdog_search_type

type of search for the watchdog step: 0 -> line search, 1 -> arcsearch, 2 -> path search

int projected_gradient_search_type

type of search for the projected gradient step: 0 -> line search, 1 -> arc search

double delta

acceptable distance between 2 iterates to qualify as d-step.

Value is updated at each iteration

double delta_var

variation of delta

double sigma

value for the line search decrease test

double alpha_min_watchdog

min value for alpha in line or arc search

double alpha_min_pgrad

min value for alpha in line or arc search

int n

current number of d_step taken

int n_max

max number of d_step taken without checking the merit value (m-step)

double ref_merit

reference value for the merit function

double merit_incr

allowed increment in the merit function for d_step

void *ref_merit_data

data struct containing the data to update the reference value

double *checkpoint

checkpoint (z_c(0), z_c(T)), of size 2*n

double delta_checkpoint

value of delta at checkpoint

double *bestpoint

best point, used for projected gradient step

double merit_bestpoint

value of the merit function at the best point

double delta_bestpoint

value of delta at best point

double *workspace

allocation memory for all the necessary computations

NumericsMatrix *H

NumericsMatrix for the computation of the jacobian matrix.

void *set

set where z is constrained

path_record *path_data

record of the path generated by the algorithm

search_data *ls_data

data for the line search