[Insight-users] Doubts in Bsplines and LBFGSOptimizer

[Popa Teo]

Some questions related to BSpline Registration
   
  Parameters of Deformableregistration6.cxx are in the form 
  
  I(Iteration) NFN  FUNC GNORM STEPLENGTH.
   
   
  Can someone tell me what these parameters represent?
   
    About LBFGS:
  At each iteration a limited memory BFGS approximation to the Hessian is updated. This limited memory matrix is used to define a quadratic model of the objective function .A search direction is then computed using a two-stage approach: first, the gradient projection method is used to identify a set of active variables, i.e. variables that will be held at their bounds; then the quadratic model is approximately minimized with respect to the free variables. The search direction is defined to be the vector leading from the current iterate to this approximate minimizer. Finally a line search is performed along the search direction . A novel feature of the algorithm is that the limited memory BFGS matrices are represented in a compact formthat is efficient for bound constrained problems. 
   

  Input parameters
  -max number. L-BFGS iterations
  -max. no. of linesearch iterations-not used in my stoping criterion
  -Step size stopping tolerance
  -Gradient stopping tolerance
   
  I belive they represent something like this:
   
  I=the number of iterations for  LBFGS-
  At each iteration ' I ' the next values are computed:
  NFN-number of  cost functional and gradient evaluation per iteration
  FUNC= values of cost functional-calculated based on Steplenght and initial cost func
  GNROM -values of gradient-calculated based on StepLenght and initial cost func
  STEPLENGHT= Quasi Newton step-computed by applying inverse of approximate Hessian to negative gradient 
   
   
  Stoping criterion for LBFGS:
  1)I>=max number. L-BFGS iterations
  2)STEPLENGHT_new/STEPLENGHT_old computed in the same iteration<Step size stopping tolerance
  3)GNROM_new/GNROM_old computed in the same iteration<Gradient stopping tolerance
  4)Maybe: NFN=max. no. of linesearch iterations not sure
   
   
   
  Based on:http://www.math.montana.edu/~vogel/Courses/M591_2000/M591_codes/lbfgs/lbfgs.m
   
   
  Teo

		
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