Date: 2015-10-02T22:30:22+00:00

Actual source code: ntl.h
petsc-3.6.2 2015-10-02
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      1: /*
      2:   Context for a Newton trust-region, line-search method for unconstrained
      3:   minimization
      4: */

      6: #ifndef __TAO_NTL_H
      8: #include <petsc/private/taoimpl.h>

     10: typedef struct {
     11:   Mat M;

     13:   Vec W;
     14:   Vec Xold;
     15:   Vec Gold;
     16:   Vec Diag;

     18:   /* Parameters when updating the trust-region radius based on steplength */
     19:   PetscReal nu1;                /* used to compute trust-region radius */
     20:   PetscReal nu2;                /* used to compute trust-region radius */
     21:   PetscReal nu3;                /* used to compute trust-region radius */
     22:   PetscReal nu4;                /* used to compute trust-region radius */

     24:   PetscReal omega1;        /* factor used for trust-region update */
     25:   PetscReal omega2;        /* factor used for trust-region update */
     26:   PetscReal omega3;        /* factor used for trust-region update */
     27:   PetscReal omega4;        /* factor used for trust-region update */
     28:   PetscReal omega5;        /* factor used for trust-region update */

     30:   /*
     31:      if   step < nu1            (very bad step)
     32:        radius = omega1 * min(norm(d), radius)
     33:      elif step < nu2            (bad step)
     34:        radius = omega2 * min(norm(d), radius)
     35:      elif step < nu3            (okay step)
     36:        radius = omega3 * radius;
     37:      elif step < nu4            (good step)
     38:        radius = max(omega4 * norm(d), radius)
     39:      else                       (very good step)
     40:        radius = max(omega5 * norm(d), radius)
     41:      fi
     42:   */

     44:   /* Parameters when updating the trust-region radius based on reduction */
     45:   PetscReal eta1;               /* used to compute trust-region radius */
     46:   PetscReal eta2;               /* used to compute trust-region radius */
     47:   PetscReal eta3;               /* used to compute trust-region radius */
     48:   PetscReal eta4;               /* used to compute trust-region radius */

     50:   PetscReal alpha1;        /* factor used for trust-region update */
     51:   PetscReal alpha2;        /* factor used for trust-region update */
     52:   PetscReal alpha3;        /* factor used for trust-region update */
     53:   PetscReal alpha4;        /* factor used for trust-region update */
     54:   PetscReal alpha5;        /* factor used for trust-region update */

     56:   /* kappa = ared / pred
     57:      if   kappa < eta1          (very bad step)
     58:        radius = alpha1 * min(norm(d), radius)
     59:      elif kappa < eta2          (bad step)
     60:        radius = alpha2 * min(norm(d), radius)
     61:      elif kappa < eta3          (okay step)
     62:        radius = alpha3 * radius;
     63:      elif kappa < eta4          (good step)
     64:        radius = max(alpha4 * norm(d), radius)
     65:      else                       (very good step)
     66:        radius = max(alpha5 * norm(d), radius)
     67:      fi
     68:   */

     70:   /* Parameters when updating the trust-region radius based on interpolation */
     71:   PetscReal mu1;                /* used for model agreement in interpolation */
     72:   PetscReal mu2;                /* used for model agreement in interpolation */

     74:   PetscReal gamma1;     /* factor used for interpolation */
     75:   PetscReal gamma2;     /* factor used for interpolation */
     76:   PetscReal gamma3;     /* factor used for interpolation */
     77:   PetscReal gamma4;     /* factor used for interpolation */

     79:   PetscReal theta;              /* factor used for interpolation */

     81:   /* kappa = ared / pred
     82:      if   kappa >= 1.0 - mu1    (very good step)
     83:        choose tau in [gamma3, gamma4]
     84:        radius = max(tau * norm(d), radius)
     85:      elif kappa >= 1.0 - mu2    (good step)
     86:        choose tau in [gamma2, gamma3]
     87:        if (tau >= 1.0)
     88:          radius = max(tau * norm(d), radius)
     89:        else
     90:          radius = tau * min(norm(d), radius)
     91:        fi
     92:      else                       (bad step)
     93:        choose tau in [gamma1, 1.0]
     94:        radius = tau * min(norm(d), radius)
     95:      fi
     96:   */

     98:   /* Parameters when initializing trust-region radius based on interpolation */
     99:   PetscReal mu1_i;              /* used for model agreement in interpolation */
    100:   PetscReal mu2_i;              /* used for model agreement in interpolation */

    102:   PetscReal gamma1_i;   /* factor used for interpolation */
    103:   PetscReal gamma2_i;   /* factor used for interpolation */
    104:   PetscReal gamma3_i;   /* factor used for interpolation */
    105:   PetscReal gamma4_i;   /* factor used for interpolation */

    107:   PetscReal theta_i;    /* factor used for interpolation */

    109:   /* Other parameters */
    110:   PetscReal min_radius;    /* lower bound on initial radius value */
    111:   PetscReal max_radius;    /* upper bound on trust region radius */
    112:   PetscReal epsilon;       /* tolerance used when computing ared/pred */

    114:   PetscInt ntrust;              /* Trust-region steps accepted */
    115:   PetscInt newt;                /* Newton directions attempted */
    116:   PetscInt bfgs;                /* BFGS directions attempted */
    117:   PetscInt sgrad;               /* Scaled gradient directions attempted */
    118:   PetscInt grad;                /* Gradient directions attempted */

    120:   PetscInt ksp_type;            /* KSP method for the code */
    121:   PetscInt pc_type;             /* Preconditioner for the code */
    122:   PetscInt bfgs_scale_type;     /* Scaling matrix to used for the bfgs preconditioner */
    123:   PetscInt init_type;   /* Trust-region initialization method */
    124:   PetscInt update_type;      /* Trust-region update method */
    125: } TAO_NTL;

    127: #endif /* ifndef __TAO_NTL_H */