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

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

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

 13:   Vec D;
 14:   Vec W;

 16:   PetscReal radius;

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

 20:      kappa = ared / pred
 21:      if   kappa < eta1          (very bad step)
 22:        radius = alpha1 * min(norm(d), radius)
 23:      elif kappa < eta2          (bad step)
 24:        radius = alpha2 * min(norm(d), radius)
 25:      elif kappa < eta3          (okay step)
 26:        radius = alpha3 * radius;
 27:      elif kappa < eta4          (good step)
 28:        radius = max(alpha4 * norm(d), radius)
 29:      else                       (very good step)
 30:        radius = max(alpha5 * norm(d), radius)
 31:      fi
 32:   */

 34:   PetscReal eta1;          /*  used to compute trust-region radius */
 35:   PetscReal eta2;          /*  used to compute trust-region radius */
 36:   PetscReal eta3;          /*  used to compute trust-region radius */
 37:   PetscReal eta4;          /*  used to compute trust-region radius */

 39:   PetscReal alpha1;        /*  factor used for trust-region update */
 40:   PetscReal alpha2;        /*  factor used for trust-region update */
 41:   PetscReal alpha3;        /*  factor used for trust-region update */
 42:   PetscReal alpha4;        /*  factor used for trust-region update */
 43:   PetscReal alpha5;        /*  factor used for trust-region update */

 45:   /* Parameters when updating the trust-region radius based on interpolation

 47:      kappa = ared / pred
 48:      if   kappa >= 1.0 - mu1    (very good step)
 49:        choose tau in [gamma3, gamma4]
 50:        radius = max(tau * norm(d), radius)
 51:      elif kappa >= 1.0 - mu2    (good step)
 52:        choose tau in [gamma2, gamma3]
 53:        if (tau >= 1.0)
 54:          radius = max(tau * norm(d), radius)
 55:        else
 56:          radius = tau * min(norm(d), radius)
 57:        fi
 58:      else                       (bad step)
 59:        choose tau in [gamma1, 1.0]
 60:        radius = tau * min(norm(d), radius)
 61:      fi
 62:   */

 64:   PetscReal mu1;           /*  used for model agreement in radius update */
 65:   PetscReal mu2;           /*  used for model agreement in radius update */

 67:   PetscReal gamma1;        /*  factor used for radius update */
 68:   PetscReal gamma2;        /*  factor used for radius update */
 69:   PetscReal gamma3;        /*  factor used for radius update */
 70:   PetscReal gamma4;        /*  factor used for radius update */

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

 74:   /* Parameters when initializing trust-region radius based on interpolation */

 76:   PetscReal mu1_i;         /*  used for model agreement in interpolation */
 77:   PetscReal mu2_i;         /*  used for model agreement in interpolation */

 79:   PetscReal gamma1_i;      /*  factor used for interpolation */
 80:   PetscReal gamma2_i;      /*  factor used for interpolation */
 81:   PetscReal gamma3_i;      /*  factor used for interpolation */
 82:   PetscReal gamma4_i;      /*  factor used for interpolation */

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

 86:   PetscReal min_radius;    /*  lower bound on initial radius value */
 87:   PetscReal max_radius;    /*  upper bound on trust region radius */
 88:   PetscReal epsilon;       /*  tolerance used when computing actred/prered */

 90:   PetscInt init_type;      /*  Trust-region initialization method */
 91:   PetscInt update_type;    /*  Trust-region update method */
 92: } TAO_NTR;

 94: #endif /* if !defined(__TAO_NTR_H) */