# File numerics/src/NonSmoothNewton.h¶

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Typedef and functions declarations related to non-smooth Newton solver

Solve $$\phi(z) = 0$$ using a Newton method.

The algorithm is alg 4.1 of the paper of Kanzow and Kleinmichel, “A new class of semismooth Newton-type methods

for nonlinear complementarity problems”, in Computational Optimization and Applications, 11, 227-251 (1998).

Typedefs

typedef void (*NewtonFunctionPtr)(int, double*, double*, int)

Enums

enum NONSMOOTH_NEWTON_SOLVER

Values:

enumerator SICONOS_NONSMOOTH_NEWTON_LSA

Functions

void linesearch_Armijo(int n, double *z, double *dir, double psi_k, double descentCondition, NewtonFunctionPtr *phi)

Armijo Linesearch.

Parameters
• n – size of the vector z

• z – unknown vector

• dir – search direction

• psi_k – initial value of the merit function

• descentCondition – descent condition

• phi – pointer to function used to compute phi(z)

int nonSmoothNewton(int n, double *z, NewtonFunctionPtr *phi, NewtonFunctionPtr *jacobianPhi, SolverOptions *options)

Newton solver with line Search.

Parameters
• n – size of the vector z

• z – unknown vector, in-out argument

• phi – pointer to $$\phi$$ function

• jacobianPhi – pointer to $$\nabla_z \phi(z)$$ function

• iparam – vector of int parameters:

•  : max. number of iterations

•  : number of iterations processed

• dparam – vector of double parameters:

• : tolerance

• : error

Returns

int 0 if ok

int nonSmoothDirectNewton(int n, double *z, NewtonFunctionPtr *phi, NewtonFunctionPtr *jacobianPhi, SolverOptions *options)

Newton solver without line Search.

Parameters
• n – size of the vector z

• z – unknown vector, in-out argument

• phi – pointer to $$\phi$$ function

• jacobianPhi – pointer to $$\nabla_z \phi(z)$$ function

• iparam – vector of int parameters:

•  : max. number of iterations

•  : number of iterations processed

• dparam – vector of double parameters:

• : tolerance

• : error

Returns

int 0 if ok

void nonSmoothNewton_set_default(SolverOptions *options)

Variables

const char *const SICONOS_NONSMOOTH_NEWTON_LSA_STR