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File numerics/src/tools/Newton_methods.h

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File numerics/src/tools/Newton_methods.h#

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Data structure and function for using Newton based solvers

The reference used for the implementation is “Finite-Dimensional Variational

Inequalities and Complementarity Problems” by Facchinei and Pang.

More precisely, the function newton_LSA() is algorithm VFBLSA.

Defines

NEWTON_STATS_ITERATION#
NEWTON_STATS_NEWTON_STEP#
NEWTON_STATS_DESC_DIR#

Typedefs

typedef void (*compute_F_ptr)(void *data_opaque, double *z, double *F)#
typedef void (*compute_F_merit_ptr)(void *data_opaque, double *z, double *F, double *F_merit)#

Enums

enum NEWTON_SOLVER#

Values:

enumerator SICONOS_NEWTON_LSA#
enum SICONOS_NEWTON_IPARAM#

Values:

enumerator SICONOS_IPARAM_LSA_NONMONOTONE_LS#

line search based algo use this

enumerator SICONOS_IPARAM_LSA_NONMONOTONE_LS_M#
enumerator SICONOS_IPARAM_LSA_FORCE_ARCSEARCH#
enumerator SICONOS_IPARAM_LSA_SEARCH_CRITERION#
enumerator SICONOS_IPARAM_STOPPING_CRITERION#
enum SICONOS_STOPPING_CRITERION#

Values:

enumerator SICONOS_STOPPING_CRITERION_RESIDU#
enumerator SICONOS_STOPPING_CRITERION_STATIONARITY#
enumerator SICONOS_STOPPING_CRITERION_RESIDU_AND_STATIONARITY#
enumerator SICONOS_STOPPING_CRITERION_USER_ROUTINE#
enum SICONOS_GOLDSTEIN_IPARAM#

Values:

enumerator SICONOS_IPARAM_GOLDSTEIN_ITERMAX#
enum SICONOS_NMS_IPARAM#

Values:

enumerator SICONOS_IPARAM_NMS_WATCHDOG_TYPE#

non-monotone specific part

enumerator SICONOS_IPARAM_NMS_PROJECTED_GRADIENT_TYPE#
enumerator SICONOS_IPARAM_NMS_N_MAX#
enum SICONOS_NEWTON_DPARAM#

Values:

enumerator SICONOS_DPARAM_LSA_ALPHA_MIN#

line-search

enumerator SICONOS_DPARAM_GOLDSTEIN_C#
enumerator SICONOS_DPARAM_GOLDSTEIN_ALPHAMAX#
enum SICONOS_NMS_DPARAM#

Values:

enumerator SICONOS_DPARAM_NMS_DELTA#

non-monotone specific part

enumerator SICONOS_DPARAM_NMS_DELTA_VAR#
enumerator SICONOS_DPARAM_NMS_SIGMA#
enumerator SICONOS_DPARAM_NMS_ALPHA_MIN_WATCHDOG#
enumerator SICONOS_DPARAM_NMS_ALPHA_MIN_PGRAD#
enumerator SICONOS_DPARAM_NMS_MERIT_INCR#

Functions

void newton_LSA(unsigned n, double *z, double *w, int *info, void *data, SolverOptions *options, functions_LSA *functions)#

Newton algorithm for finding the zero of a function with a line search.

Mainly used for equation-based reformulation of CP or VI.

Parameters:

  • n – size of the problem

  • z – variable

  • w – value of F(z)

  • info – solver-specific values

  • data – opaque problem definition

  • options – options for this solver

  • functions – struct of function pointers to compute F, H and the error

static inline void init_lsa_functions(functions_LSA *functions, compute_F_ptr compute_F, compute_F_merit_ptr merit_function)#

Set the functions to compute F and F_merit and all the other pointers to NULL.

Parameters:

  • functions – structure to fill

  • compute_F – function to compute F

  • merit_function – function to compute F_merit

void set_lsa_params_data(SolverOptions *options, NumericsMatrix *mat)#

Set the parameters and data for newton_LSA.

Parameters:

  • options – the solver option

  • mat – the

void newton_LSA_free_solverOptions(SolverOptions *options)#

clear the solver-specific data

Parameters:

options – the SolverOption structure

void newton_lsa_set_default(SolverOptions *options)#

Variables

const char *const SICONOS_NEWTON_LSA_STR#
struct functions_LSA#
#include <Newton_methods.h>

Struct holding the necessary pointers to functions needed by the newton_LSA() procedure.

Public Members

compute_F_ptr compute_F#

function to evaluate w = F(z)

compute_F_merit_ptr compute_F_merit#

function to evaluate F_merit(z) (e.g.

F_FB, F_{min}, …)

void (*compute_H)(void *data_opaque, double *z, double *w, double *workV1, double *workV2, NumericsMatrix *H)#

function to get an element H of T

void (*compute_error)(void *data_opaque, double *z, double *w, double *nabla_theta, double tol, double *err)#

function to compute the error

void (*compute_RHS_desc)(void *data_opaque, double *z, double *w, double *F_desc)#

function to evaluate F_desc(z) (e.g.

F_FB, F_{min}, …), optional

void (*compute_H_desc)(void *data_opaque, double *z, double *w, double *workV1, double *workV2, NumericsMatrix *H_desc)#

function to get an element H_desc of T_desc, optional

int (*compute_descent_direction)(void *data_opaque, double *z, double *w, double *descent_dir, SolverOptions *options)#

function to get the descent direction, used for instance in the Newton-Josephy method

void (*compute_JacTheta_merit)(void *data_opaque, double *z, double *w, double *F_merit, double *workV, double *JacThetaF_merit, SolverOptions *options)#

function to get the descent direction, used for instance in the Newton-Josephy method

void *(*get_set_from_problem_data)(void *problem)#

Function returning the set description from the

int (*ls_failure_fn)(void *problem, double *z, double *w, double *descent_dir, double err, size_t status)#

Function to call when the line search fails.

struct newton_stats#

Public Members

int id#

id of this structure

double merit_value#

value of the merit function at the end of the iteration

double alpha#

value of the LS parameter

unsigned int status#

status of this newton iteration

struct newton_LSA_param#

Public Members

double p#

p value for the acceptance test of the direction solution of the linear system

double sigma#

ratio for the decrease in norm of the C-function ( \( gamma' \) in VFBLSA)

double rho#

coefficient for the direction check

bool keep_H#

keep the matrix H untouched.

Only used in the dense case, where a copy of the matrix is factorized

bool check_dir_quality#

Check the quality of the descent direction (Eqn 9.1.6 p.

805 in Facchinei & Pang)

struct newton_LSA_data#

Public Members

NumericsMatrix *H#

matrix

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