<DIV>Some questions related to BSpline Registration</DIV> <DIV> </DIV> <DIV>Parameters of Deformableregistration6.cxx are in the form </DIV> <DIV><BR> I(Iteration) NFN FUNC GNORM STEPLENGTH.</DIV> <DIV> </DIV> <DIV> </DIV> <DIV>Can someone tell me what these parameters represent?</DIV> <DIV> </DIV> <DIV> <DIV><U>About LBFGS:</U></DIV> <DIV><!--StartFragment -->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. </DIV> <DIV> </DIV></DIV> <DIV><U>Input parameters</U></DIV> <DIV>-max number. L-BFGS iterations</DIV> <DIV>-max. no. of linesearch iterations-not used in my stoping criterion</DIV> <DIV>-Step size stopping tolerance</DIV> <DIV>-Gradient stopping tolerance</DIV> <DIV> </DIV> <DIV>I belive they represent something like this:</DIV> <DIV> </DIV> <DIV>I=the number of iterations for LBFGS-</DIV> <DIV>At each iteration ' I ' the next values are computed:</DIV> <DIV>NFN-number of cost functional and gradient evaluation per iteration</DIV> <DIV>FUNC= values of cost functional-calculated based on Steplenght and initial cost func</DIV> <DIV>GNROM -<!--StartFragment -->values of gradient-calculated based on StepLenght and initial
cost func</DIV> <DIV>STEPLENGHT= Quasi Newton step-computed by applying inverse of approximate Hessian to negative gradient </DIV> <DIV> </DIV> <DIV> </DIV> <DIV>Stoping criterion for LBFGS:</DIV> <DIV>1)I>=max number. L-BFGS iterations</DIV> <DIV>2)STEPLENGHT_new/STEPLENGHT_old computed in the same iteration<Step size stopping tolerance</DIV> <DIV>3)GNROM_new/GNROM_old computed in the same iteration<Gradient stopping tolerance</DIV> <DIV>4)Maybe: NFN=max. no. of linesearch iterations not sure</DIV> <DIV> </DIV> <DIV> </DIV> <DIV> </DIV> <DIV>Based on:http://www.math.montana.edu/~vogel/Courses/M591_2000/M591_codes/lbfgs/lbfgs.m</DIV> <DIV> </DIV> <DIV> </DIV> <DIV>Teo</DIV><p>
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