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 */