TaoConvergedReason#

reason a Tao optimizer was said to have converged or diverged

Synopsis#

typedef enum {               /* converged */
  TAO_CONVERGED_GATOL   = 3, /* ||g(X)|| < gatol */
  TAO_CONVERGED_GRTOL   = 4, /* ||g(X)|| / f(X)  < grtol */
  TAO_CONVERGED_GTTOL   = 5, /* ||g(X)|| / ||g(X0)|| < gttol */
  TAO_CONVERGED_STEPTOL = 6, /* step size small */
  TAO_CONVERGED_MINF    = 7, /* F < F_min */
  TAO_CONVERGED_USER    = 8, /* User defined */
  /* diverged */
  TAO_DIVERGED_MAXITS       = -2,
  TAO_DIVERGED_NAN          = -4,
  TAO_DIVERGED_MAXFCN       = -5,
  TAO_DIVERGED_LS_FAILURE   = -6,
  TAO_DIVERGED_TR_REDUCTION = -7,
  TAO_DIVERGED_USER         = -8, /* User defined */
  /* keep going */
  TAO_CONTINUE_ITERATING = 0
} TaoConvergedReason;

Values#

TAO_CONVERGED_GATOL - \(||g(X)|| < gatol\)
TAO_CONVERGED_GRTOL - \(||g(X)|| / f(X) < grtol\)
TAO_CONVERGED_GTTOL - \(||g(X)|| / ||g(X0)|| < gttol\)
TAO_CONVERGED_STEPTOL - step size smaller than tolerance
TAO_CONVERGED_MINF - \(F < F_min\)
TAO_CONVERGED_USER - the user indicates the optimization has succeeded
TAO_DIVERGED_MAXITS - the maximum number of iterations allowed has been achieved
TAO_DIVERGED_NAN - not a number appeared in the computations
TAO_DIVERGED_MAXFCN - the maximum number of function evaluations has been computed
TAO_DIVERGED_LS_FAILURE - a linesearch failed
TAO_DIVERGED_TR_REDUCTION - trust region failure
TAO_DIVERGED_USER - the user has indicated the optimization has failed
TAO_CONTINUE_ITERATING - the optimization is still running, TaoSolve()

where

X - current solution
X0 - initial guess
f(X) - current function value
f(X) -* true solution (estimated)
g(X) - current gradient
its - current iterate number
maxits - maximum number of iterates
fevals - number of function evaluations
max_funcsals - maximum number of function evaluations

Note#

The two most common reasons for divergence are an incorrectly coded or computed gradient or Hessian failure or lack of convergence in the linear system solve (in this case we recommend testing with -pc_type lu to eliminate the linear solver as the cause of the problem).