Actual source code: ntlimpl.h

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

     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 grad;   /* Gradient directions attempted */

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