1: /*
  2:   Context for a Newton trust region method (unconstrained minimization)
  3: */

  5: #ifndef __TAO_NTR_H
  7: #include <petsc/private/taoimpl.h>

  9: typedef struct {
 10:   Mat M;

 12:   Vec D;
 13:   Vec W;

 15:   Vec Diag;
 16:   PetscReal radius;
 17:   /*  Parameters when updating the trust-region radius based on reduction */
 18:   PetscReal eta1;          /*  used to compute trust-region radius */
 19:   PetscReal eta2;          /*  used to compute trust-region radius */
 20:   PetscReal eta3;          /*  used to compute trust-region radius */
 21:   PetscReal eta4;          /*  used to compute trust-region radius */

 23:   PetscReal alpha1;     /*  factor used for trust-region update */
 24:   PetscReal alpha2;     /*  factor used for trust-region update */
 25:   PetscReal alpha3;     /*  factor used for trust-region update */
 26:   PetscReal alpha4;     /*  factor used for trust-region update */
 27:   PetscReal alpha5;     /*  factor used for trust-region update */

 29:   /*
 30:      kappa = ared / pred
 31:      if   kappa < eta1          (very bad step)
 32:        radius = alpha1 * min(norm(d), radius)
 33:      elif kappa < eta2          (bad step)
 34:        radius = alpha2 * min(norm(d), radius)
 35:      elif kappa < eta3          (okay step)
 36:        radius = alpha3 * radius;
 37:      elif kappa < eta4          (good step)
 38:        radius = max(alpha4 * norm(d), radius)
 39:      else                       (very good step)
 40:        radius = max(alpha5 * norm(d), radius)
 41:      fi
 42:   */
 43:   /*  Parameters when updating the trust-region radius based on interpolation */
 44:   PetscReal mu1;                /*  used for model agreement in radius update */
 45:   PetscReal mu2;                /*  used for model agreement in radius update */

 47:   PetscReal gamma1;     /*  factor used for radius update */
 48:   PetscReal gamma2;     /*  factor used for radius update */
 49:   PetscReal gamma3;     /*  factor used for radius update */
 50:   PetscReal gamma4;     /*  factor used for radius update */

 52:   PetscReal theta;              /*  factor used for radius update */

 54:   /*
 55:      kappa = ared / pred
 56:      if   kappa >= 1.0 - mu1    (very good step)
 57:        choose tau in [gamma3, gamma4]
 58:        radius = max(tau * norm(d), radius)
 59:      elif kappa >= 1.0 - mu2    (good step)
 60:        choose tau in [gamma2, gamma3]
 61:        if (tau >= 1.0)
 62:          radius = max(tau * norm(d), radius)
 63:        else
 64:          radius = tau * min(norm(d), radius)
 65:        fi
 66:      else                       (bad step)
 67:        choose tau in [gamma1, 1.0]
 68:        radius = tau * min(norm(d), radius)
 69:      fi
 70:   */

 72:   /*  Parameters when initializing trust-region radius based on interpolation */
 73:   PetscReal mu1_i;         /*  used for model agreement in interpolation */
 74:   PetscReal mu2_i;         /*  used for model agreement in interpolation */

 76:   PetscReal gamma1_i;      /*  factor used for interpolation */
 77:   PetscReal gamma2_i;      /*  factor used for interpolation */
 78:   PetscReal gamma3_i;      /*  factor used for interpolation */
 79:   PetscReal gamma4_i;      /*  factor used for interpolation */

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

 83:   PetscReal min_radius; /*  lower bound on initial radius value */
 84:   PetscReal max_radius; /*  upper bound on trust region radius */
 85:   PetscReal epsilon;    /*  tolerance used when computing actred/prered */

 87:   PetscInt ksp_type;         /*  KSP method for the code */
 88:   PetscInt pc_type;          /*  Preconditioner for the code */
 89:   PetscInt bfgs_scale_type;  /*  Scaling matrix for the bfgs preconditioner */
 90:   PetscInt init_type;   /*  Trust-region initialization method */
 91:   PetscInt update_type; /*  Trust-region update method */
 92: } TAO_NTR;

 94: #endif /* ifndef __TAO_NTR_H */