function minimum evaluation problem

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Sri 2014-9-30

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I have a function which is f(r) = (2^(r/w)-1)*a+b+(c/r), where a, b, c are constants and r is lower bounded by 20000.

I have evaluated using fmincon and also by using fzero and fsolve for f'(r) (differentiation of f(r)). The code is given below.

w = 20000;
No = .000001;%
% No = 10^(-20);
myu = 1000;
% rho = .1;
rho = .50;
btr = 5;
mean_bt = 1/btr;
tou = 0;
a = No*myu/rho;
%direct minimum
opt = optimoptions('fmincon', 'Algorithm', 'interior-point');
[x,fval,exitflag] = fmincon(@(r) (2^(r/w)-1)*a+mean_bt+(myu/r), 20000,[],[],[],[],20000,Inf, [], opt)
fsOpts = optimoptions('fsolve', 'MaxFunEvals', 1000, 'TolFun', 10^-9)
[r, fval, exitflag] = fsolve(@(r) (2^(r/w)*(a/w)*log(2))-(myu/r^2), 20000, fsOpts)
[optp,fval, exitflag] = fzero(@(r) (2^(r/w)*(a/w)*log(2))-(myu/r^2), 20000)

I am getting different values with different solvers. 1. With fmincon, I got 3.1969e+04, but it is observed that with 3.2100e+04, I am getting even lower value. I thought probably local minimum could be a reason, but it is not clear. 2. with fsolve, whatever inital value, I am getting the same value? 3. With fzero, I am getting 5.0267e+04 and it seems to be correct.

Could someone kindly explain me the possible reasons for the above behavior and correct ways to use solvers properly?