Good Day Mathwork Community; I have the following code for returning the strong wolfe line search in soliving conjugate gradient method unconstrained optimization, iam find

Good Day Mathwork Community;

I have the following code for returning the strong wolfe line search in soliving conjugate gradient method unconstrained optimization, iam finding it difficult to return number function evaluations (nfval) and gradient evalution (ngval). Can some one assist me with the solution of these problems

Thanks

Nasiru Salihu

function [alpha, x, f, grad, fail, nsteps] = St_Wolfe(x0,d,op)

c1 = 1e-4;

c2 = -0.00001;

%c1 = .01;

%c2 = 0.9;

%c1 = 1e-4;

%c2 = 0.001;

%c1 = 0.0001

%c2 = 0.9;

f0=test_functions(x0,op);

grad0=test_functions(x0,op,1);

g0 = grad0'*d;

if g0 >= 0

error('g0 must be negative, not a descent direction')

end

old = 0; fold = f0; gold = g0;

new = 1;

nexpand = max([50 -round(log2(norm(d)))]);

for k = 1:nexpand

xnew = x0 + new*d;

fnew=test_functions(xnew,op);

gradnew=test_functions(xnew,op,1);

gnew = gradnew'*d;

if fnew > f0 + c1*new*g0 | ((fnew >= fold) & k > 1) %

[alpha, x, f, grad, fail, nsteps] = zoom1(old, new, ...

fold, fnew, gold, gnew, f0, g0, x0, d,op, c1, c2);

return

end

if abs(gnew) <= c2*g0

alpha = new; x = xnew; f = fnew; grad = gradnew; fail = 0; nsteps = k;

return

end

if gnew >= 0

[alpha, x, f, grad, fail, nsteps] = zoom1(new, old, ...

fnew, fold, gnew, gold, f0, g0, x0, d,op, c1, c2);

return

end

old = new;

fold = fnew;

gold = gnew;

new = 2*new;

end

alpha = new;

x = xnew;

f = fnew;

grad = gradnew;

fail = -1;

nsteps = 0;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [alpha, x, f, grad, fail, nsteps] = zoom1(...

lo, hi, flo, fhi, glo, ghi, f0, g0, x0, d,op, c1, c2)

fail = 0;

lo2 = hi;

flo2 = fhi;

glo2 = ghi;

nsteps = 0;

while lo ~= hi & nsteps < 50

nsteps = nsteps + 1;

bisect = (lo + hi)/2;

interp = cubic_interp(lo, lo2, flo, flo2, glo, glo2);

if inside(interp, lo, bisect)

atry = interp;

else

atry = bisect;

end;

xtry = x0 + atry*d;

ftry=test_functions(xtry,op);

gradtry=test_functions(xtry,op,1);

gtry = gradtry'*d;

if ftry > f0 + c1*atry*g0 | ftry >= flo

hi = atry;

lo2 = hi; flo2 = ftry; glo2 = gtry;

else

if abs(gtry) <= -c2*g0

alpha = atry; x = xtry; f = ftry; grad = gradtry;

return

end

if gtry*(hi - lo) >= 0

hi = lo;

end

lo2 = lo; flo2 = flo; glo2 = glo;

lo = atry; flo = ftry; glo = gtry;

end

end

alpha = atry; x = xtry; f = ftry; grad = gradtry; fail = 1;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function xmin = cubic_interp(x1, x2, f1, f2, g1, g2)

eta = g1 + g2 - 3*(f1 - f2)/(x1 - x2);

gamma = sign(x2-x1)*sqrt(eta^2 - g1*g2);

xmin = x2 - (x2 - x1)*(g2 + gamma - eta)/(g2 - g1 + 2*gamma);

Answer 1

[Umang Pandey]

Hi Nasiru,

I understand that you want to count the number of function evaluations (nfval) and number of gradient evaluations (ngval) in your code.

This can be achieved by modifying the function definitions to include the "ngval" and "nfval" variables, in the following manner:

1. Initialize the "nfval" and "ngval" variables in the "St_Wolfe" function:

function [alpha, x, f, grad, fail, nsteps, nfval, ngval] = St_Wolfe(x0,d,op) 
nfval = 0; 
ngval = 0; 
% Your custom code... 

2. Modify the "test_functions", "zoom1" and "cubic_interp" functions to pass and update the "nfval" and "ngval" variables within these functions whenever they are called and gradients are calculated:

function [xmin, nfval, ngval] = cubic_interp(x1, x2, f1, f2, g1, g2, nfval, ngval) 

    nfval = nfval + 1; 
    % Your custom code... 

function [alpha, x, f, grad, fail, nsteps, nfval, ngval] = zoom1(... 
    lo, hi, flo, fhi, glo, ghi, f0, g0, x0, d,op, c1, c2, nfval, ngval) 

    nfval = nfval + 1; 
    % Your custom code... 

Best,

Umang