___________________________________________________________________
 |                                                                 |
 |                               HESSIAN                           |
 |_________________________________________________________________|

 MEANING: A matrix computed by NONMEM
 CONTEXT: NONMEM output

 DISCUSSION:

 The Hessian matrix is the second derivative matrix  of  the  objective
 function with respect to the parameters of the model.  NONMEM computes
 Hessian matrices for several purposes.

 Estimation Step
      A rough numerical approximation to the Hessian is maintained dur-
      ing the minimization search.  The following message in the inter-
      mediate output refers to this matrix:

      RESET HESSIAN

      Explanation:  The search starts with the Hessian set to the iden-
      tity matrix. The Hessian is updated after each iteration, using a
      rank 1 update procedure. When  there  is  no  longer  a  sensible
      direction  to  take,  but convergence has not been achieved, this
      may be due to inadequacy of the updated Hessian. Then the Hessian
      is reset to a certain positive semi-definite diagonal matrix, and
      a new direction computed from this matrix (and the gradient  vec-
      tor) is tried.

      The appearance of the message indicates why  an  unusually  large
      number of function evaluations were used for the iteration (extra
      ones were needed to compute the new Hessian and  perform  a  line
      search  along  the  new  direction) and why an unusually long CPU
      time was needed for the  iteration  (if  intermediate  output  is
      being  monitored). Its appearance suggests that the search is not
      going easily, and perhaps (not necessarily) something is wrong.

 Covariance Step
      A good numerical approximation to the Hessian is computed at  the
      final parameter estimates. It is referred to as the R matrix.

 Obtaining Conditional Estimates
      In this case, the Hessian matrix is the second derivative  matrix
      of  the conditional objective function.  The following error mes-
      sages refer to this matrix:

      HESSIAN OF OBJ. FUNCT. FOR COMPUTING CONDITIONAL ESTIMATE IS
      NON POSITIVE DEFINITE

      NUMERICAL HESSIAN OF OBJ. FUNC. ...

REFERENCES: Guide IV Section III.B.15
REFERENCES: Guide V Section 12.4.6
REFERENCES: Guide VII Section II.A


  
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