[petsc-users] TAO: armijo condition not fulfilled

[Andreas Mang]

Hey Jason:

The line search fails. If I use Armijo I get

TaoLineSearch Object:
  type: armijo
      maxf=30, ftol=1e-10, gtol=0.0001
      Armijo linesearch    : alpha=1 beta=0.5     sigma=0.0001     memsize=1
  maximum function evaluations=30
  tolerances: ftol=0.0001, rtol=1e-10, gtol=0.9
  total number of function evaluations=1
  total number of gradient evaluations=1
  total number of function/gradient evaluations=0
  Termination reason: 0

The parameters seem to be the default ones also suggested by Nocedal and Wright. So I did not change anything. The termination reason is equivalent to TAOLINESEARCH_CONTINUE_ITERATING. I am not checking the reason directly. I guess it starts reducing the step size after that. I can see that my objective function get’s evaluated (as expected); however, the objective values increase (from what I see when monitoring the evaluations of my objective). This leads to a failure in the line search and made (still makes) me believe there is a bug on my side (which I have not found yet). However, if I use a unit step it converges (relative change of the gradient e.g. to 1E-9; see bottom of this email).  If I use More & Thuente, same thing. No reduction in step size necessary.

If you suggest that I should do some further testing on simpler problems, I’m happy to do so. After looking at the code, I just felt like there obviously is something wrong in the line-search implementation.

Thanks for your help.
/Andreas

Here’s the output after the first iteration (where the Armijo line search fails):

TaoLineSearch Object:
  type: armijo
      maxf=30, ftol=1e-10, gtol=0.0001
      Armijo linesearch    : alpha=1 beta=0.5     sigma=0.0001     memsize=1
  maximum function evaluations=30
  tolerances: ftol=0.0001, rtol=1e-10, gtol=0.9
  total number of function evaluations=1
  total number of gradient evaluations=1
  total number of function/gradient evaluations=0
  Termination reason: 0
TaoLineSearch Object:
  type: armijo
      maxf=30, ftol=1e-10, gtol=0.0001
      Armijo linesearch    : alpha=1 beta=0.5     sigma=0.0001     memsize=1
  maximum function evaluations=30
  tolerances: ftol=0.0001, rtol=1e-10, gtol=0.9
  total number of function evaluations=30
  total number of gradient evaluations=0
  total number of function/gradient evaluations=0
  Termination reason: 4

With final output (end of optimization):

Tao Object: 1 MPI processes
  type: nls
      Newton steps: 1
      BFGS steps: 0
      Scaled gradient steps: 0
      Gradient steps: 1
      nls ksp atol: 0
      nls ksp rtol: 1
      nls ksp ctol: 0
      nls ksp negc: 0
      nls ksp dtol: 0
      nls ksp iter: 0
      nls ksp othr: 0
  TaoLineSearch Object:   1 MPI processes
    type: armijo
  KSP Object:   1 MPI processes
    type: cg
  total KSP iterations: 21
  convergence tolerances: fatol=0,   frtol=0
  convergence tolerances: gatol=0,   steptol=0,   gttol=0.0001
  Residual in Function/Gradient:=0.038741
  Objective value=0.639121
  total number of iterations=0,                          (max: 50)
  total number of function evaluations=31,                  max: 10000
  total number of gradient evaluations=1,                  max: 10000
  total number of function/gradient evaluations=1,      (max: 10000)
  total number of Hessian evaluations=1
  Solver terminated: -6   Line Search Failure

This is without line-search (unit step size):

Tao Object: 1 MPI processes
  type: nls
      Newton steps: 3
      BFGS steps: 0
      Scaled gradient steps: 0
      Gradient steps: 0
      nls ksp atol: 0
      nls ksp rtol: 3
      nls ksp ctol: 0
      nls ksp negc: 0
      nls ksp dtol: 0
      nls ksp iter: 0
      nls ksp othr: 0
  TaoLineSearch Object:   1 MPI processes
    type: unit
  KSP Object:   1 MPI processes
    type: cg
  total KSP iterations: 71
  convergence tolerances: fatol=0,   frtol=0
  convergence tolerances: gatol=0,   steptol=0,   gttol=0.0001
  Residual in Function/Gradient:=1.91135e-11
  Objective value=0.160914
  total number of iterations=3,                          (max: 50)
  total number of function/gradient evaluations=4,      (max: 10000)
  total number of Hessian evaluations=3
  Solution converged:    ||g(X)||/||g(X0)|| <= gttol

 

> On Jun 11, 2015, at 12:44 PM, Jason Sarich <jason.sarich at gmail.com <mailto:jason.sarich at gmail.com>> wrote:
> 
> Hi Andreas,
> 
> Yes it looks like a bug that the reason is never set, but the line should still terminate. Is the problem you are having with the line search itself, or is it failing because you are checking this ls->reason directly?
> 
> Jason Sarich
> 
> 
> On Thu, Jun 11, 2015 at 9:53 AM, Andreas Mang <andreas at ices.utexas.edu <mailto:andreas at ices.utexas.edu>> wrote:
> Hi guys:
> 
> I have a problem with the TAO Armijo line search (petsc-3.5.4). My algorithm works if I use the More & Thuente line search (default). I have numerically checked the gradient of my objective. It’s correct. I am happy to write a small snippet of code and do an easy test if you guys disagree, but from what I’ve seen in the line search code it seems obvious to me that there is a bug. Am I missing something or are you not setting
> 
> ls->reason
> 
> to
> 
> TAOLINESEARCH_SUCCESS
> 
> if the Armijo condition is fulfilled (TaoLineSearchApply_Armijo in armijo.c; line 118 - 302)?!
> 
> It seems to me that ls->reason is and will remain to be set to
> 
> TAOLINESEARCH_CONTINUE_ITERATING
> 
> if everything works (i.e. I don’t hit one of the exceptions). Does this make sense? If not I’ll invest the time and put together a simple test case and, if that works, continue to check my code.
> 
> /Andreas
> 
> 
> 

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