# File numerics/src/LCP/lcp_newton_FB.h¶

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functions to solve LCP using a Newton method on the nonsmooth equation reformulation

Functions

void FB_compute_error_lcp(void *data_opaque, double *z, double *w, double *notused, double tol, double *err)

Compute the error for termination, here lcp_compute_error.

Parameters
• data_opaque: a LinearComplementarityProblem but casted

• [in] z: non-basic variable

• [in] w: basic variable

• notused: not used here

• [in] tol: the tolerance

• [out] err: the error on the LCP (not FB)

void FB_compute_F_lcp(void *data_opaque, double *z, double *w)

Compute F(z) = Mz + q.

Parameters
• data_opaque: a LinearComplementarityProblem but casted

• [in] z: non-basic variable

• [out] w: basic variable (result)

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

Compute an element of JacF_FB, see FacchineiPang p.

808

Parameters
• data_opaque: a LinearComplementarityProblem but casted

• [in] z: non-basic variable

• [in] w: basic variable

• workV1: work vector which contains “z”

• workV2: work vector

• [out] H: an element of JacF_FB

void lcp_FB(void *data_opaque, double *z, double *F, double *F_FB)

Compute F_FB : $${F_FB}_i = \sqrt(z_i^2 + F_i^2) - (z_i + F_i)$$.

Parameters
• data_opaque: a LinearComplementarityProblem but casted

• [in] z: current value for z

• [in] F: current value for w

• [out] F_FB: value of the function