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 <>

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