1: /*
  2:   Context for a Newton trust-region, line-search method for unconstrained
  3:   minimization
  4: */

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

 10: typedef struct {
 11:   Mat M;
 12:   PC bfgs_pre;

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

 18:   /* Parameters when updating the trust-region radius based on steplength

 20:      if   step < nu1            (very bad step)
 21:        radius = omega1 * min(norm(d), radius)
 22:      elif step < nu2            (bad step)
 23:        radius = omega2 * min(norm(d), radius)
 24:      elif step < nu3            (okay step)
 25:        radius = omega3 * radius;
 26:      elif step < nu4            (good step)
 27:        radius = max(omega4 * norm(d), radius)
 28:      else                       (very good step)
 29:        radius = max(omega5 * norm(d), radius)
 30:      fi
 31:   */

 33:   PetscReal nu1;                /* used to compute trust-region radius */
 34:   PetscReal nu2;                /* used to compute trust-region radius */
 35:   PetscReal nu3;                /* used to compute trust-region radius */
 36:   PetscReal nu4;                /* used to compute trust-region radius */

 38:   PetscReal omega1;             /* factor used for trust-region update */
 39:   PetscReal omega2;             /* factor used for trust-region update */
 40:   PetscReal omega3;             /* factor used for trust-region update */
 41:   PetscReal omega4;             /* factor used for trust-region update */
 42:   PetscReal omega5;             /* factor used for trust-region update */

 44:   /* Parameters when updating the trust-region radius based on reduction

 46:      kappa = ared / pred
 47:      if   kappa < eta1          (very bad step)
 48:        radius = alpha1 * min(norm(d), radius)
 49:      elif kappa < eta2          (bad step)
 50:        radius = alpha2 * min(norm(d), radius)
 51:      elif kappa < eta3          (okay step)
 52:        radius = alpha3 * radius;
 53:      elif kappa < eta4          (good step)
 54:        radius = max(alpha4 * norm(d), radius)
 55:      else                       (very good step)
 56:        radius = max(alpha5 * norm(d), radius)
 57:      fi
 58:   */

 60:   PetscReal eta1;               /* used to compute trust-region radius */
 61:   PetscReal eta2;               /* used to compute trust-region radius */
 62:   PetscReal eta3;               /* used to compute trust-region radius */
 63:   PetscReal eta4;               /* used to compute trust-region radius */

 65:   PetscReal alpha1;             /* factor used for trust-region update */
 66:   PetscReal alpha2;             /* factor used for trust-region update */
 67:   PetscReal alpha3;             /* factor used for trust-region update */
 68:   PetscReal alpha4;             /* factor used for trust-region update */
 69:   PetscReal alpha5;             /* factor used for trust-region update */

 71:   /* Parameters when updating the trust-region radius based on interpolation
 72:      kappa = ared / pred
 73:      if   kappa >= 1.0 - mu1    (very good step)
 74:        choose tau in [gamma3, gamma4]
 75:        radius = max(tau * norm(d), radius)
 76:      elif kappa >= 1.0 - mu2    (good step)
 77:        choose tau in [gamma2, gamma3]
 78:        if (tau >= 1.0)
 79:          radius = max(tau * norm(d), radius)
 80:        else
 81:          radius = tau * min(norm(d), radius)
 82:        fi
 83:      else                       (bad step)
 84:        choose tau in [gamma1, 1.0]
 85:        radius = tau * min(norm(d), radius)
 86:      fi
 87:   */

 89:   PetscReal mu1;                /* used for model agreement in interpolation */
 90:   PetscReal mu2;                /* used for model agreement in interpolation */

 92:   PetscReal gamma1;             /* factor used for interpolation */
 93:   PetscReal gamma2;             /* factor used for interpolation */
 94:   PetscReal gamma3;             /* factor used for interpolation */
 95:   PetscReal gamma4;             /* factor used for interpolation */

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

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

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

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

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

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

120:   PetscInt init_type;           /* Trust-region initialization method */
121:   PetscInt update_type;         /* Trust-region update method */
122: } TAO_NTL;

124: #endif /* if !defined(__TAO_NTL_H) */