matlab: minimization/optimization algorithm -

i use function multiple outputs farina4 computes coefficients a, b, e, f , vector out_p5tads_final (1 x n array) through minimization of system of equations using data input set p5tads (1 x n array):

function  [a b e f fval out_p5tads_final] = farina4(p5tads)  f = @(coeff)calculs_farina4(coeff,p5tads); [ans,fval] = fminsearchcon(f,coeff0,[0 0 0 0],[1 1 1 1]);% fminsearch constrains = ans(1); b = ans(2); e = ans(3); f = ans(4);  out_p5tads_final = p5tads_farina4(a,b,e,f);  function out_coeff = calculs_farina4(coeff0,p5tads)     %bla-bla-bla end  function out_p5tads = p5tads_farina4(a,b,e,f)     %bla-bla-bla end end 

after calculating a, b, e, f , out_p5tads_final need calculate/minimize rms function respect out_p5tads_f4.

rms = sqrt(mean((p5tads(:) - out_p5tads_f4(:)).^2))*100 

and repeat function farina4 in order find optimal set of parameters a, b, e, f , out_p5tads_final.

i trying build algorithm of such optimization , not see way far. instance, seems not possible introduce function multiple output inside above rms equation unless there way index somehow output of function farina4. if there can alternative optimization algorithm rms without fminsearch (or similar) ?

a b e , f values between 0 , 1 out_p5tads_final (1 x 10) array

% function out_coeff = calculs_farina4(coeff0,p5tads)  %  mmmm = p5tads(1);  mmmr = p5tads(2);  rmmr = p5tads(3);  mmrm = p5tads(4);  mmrr = p5tads(5);  rmrm = p5tads(6);  rmrr = p5tads(7);  mrrm = p5tads(8);  mrrr = p5tads(9);  rrrr = p5tads(10);  %  = coeff0(1);  b = coeff0(2);  e = coeff0(3);  f = coeff0(4);  %  f_mmmm = mmmm - ((a^2*b^2*(a + b) + e^2*f^2*(e + f))/2);  f_mmmr = mmmr - (a^2*b^2*(e + f) + e^2*f^2*(a + b));  f_rmmr = rmmr - ((a^2*f^2*(b + e) + b^2*e^2*(a + f))/2);   f_mmrm = mmrm - 2*a*b*e*f;  f_mmrr = mmrr - b*f*(a^3 + e^3) + a*e*(a^3 + f^3);  f_rmrm = rmrm - 2*a*b*e*f;  f_rmrr = rmrr - 2*a*b*e*f;  f_mrrm = mrrm - ((a^2*b^2*(e + f) + e^2*f^2*(a + b))/2);  f_mrrr = mrrr - (a^2*f^2*(b + e) + b^2*e^2*(a + f));  f_rrrr = rrrr - ((a^2*f^2*(a + f) + b^2*e^2*(b + e))/2);  %  out_coeff = f_mmmm^2 + f_mmmr^2 + f_rmmr^2 + f_mmrm^2 + f_mmrr^2 + f_rmrm^2 + f_rmrr^2 + f_mrrm^2 + f_mrrr^2 + f_rrrr^2;  end  % function out_p5tads = p5tads_farina4(a,b,e,f)  %  p_mmmm = ((a^2*b^2*(a + b) + e^2*f^2*(e + f))/2);  p_mmmr = (a^2*b^2*(e + f) + e^2*f^2*(a + b));  p_rmmr = ((a^2*f^2*(b + e) + b^2*e^2*(a + f))/2);   p_mmrm = 2*a*b*e*f;  p_mmrr = b*f*(a^3 + e^3) + a*e*(a^3 + f^3);  p_rmrm = 2*a*b*e*f;  p_rmrr = 2*a*b*e*f;  p_mrrm = ((a^2*b^2*(e + f) + e^2*f^2*(a + b))/2);  p_mrrr = (a^2*f^2*(b + e) + b^2*e^2*(a + f));  p_rrrr = ((a^2*f^2*(a + f) + b^2*e^2*(b + e))/2);  %  out_p5tads = [p_mmmm,p_mmmr,p_rmmr,p_mmrm,p_mmrr,p_rmrm,p_rmrr,p_mrrm,p_mrrr,p_rrrr];  end  end 

thanks in advance !

19/08/2014 3:35 pm

i need optimal set of coefficients b e f rms value , calculated from

rms = sqrt(mean((p5tads(:) - out_p5tads_f4(:)).^2))*100 

is minimal. here, vector p5tads used calculate/optimize set of b e f coefficients, in turn used calculate vector out_p5tads_f4. code should run desired number of optimizations cycles (e.g. default 100) , select series of b e f , out_p5tads_f4 afforded minimal rms error value (with respect out_p5tads_f4).