I've got an constrained optimisation problem, thus I adopted the function ‘fmincon’.
The curve of the f(x) is like the figure below (This is just 1 specific case as the coefficients of f(x) would vary from case to case but the form is the same) , and we can see the minimum point is around the labelled one at x=7.1e-12.
zoom in →
However, the optimisation would stop at x=5e-12 (with initial x=1e-11) because the ‘step tolerance’ is satisfied with the default algorithm 'interior-point’. After that, no matter how I decrease the step tolerance (shown in the figure below), the function just yields the same results (x=5e-12).
Then I tried algorithm ’sqp’, the step length became too small at the 3rd row, and the function just cannot get out from ‘fval=1.017079’ after that (don't forget the f_min=0.09793 approximately at x=7.1e-12), and it seems the optimisation would just never stop (shown below).
Finally, I tried 'active-set’ algorithm, it also gives me x=5e-12. Could anyone please tell me how to push the optimisation closer to the optimal point (x=7.1e-12)? Peronally the initial point is OK. Did I do something wrong in the optimisation?
fun_2Gmm=@(t) C_Gmm1(1).*t.*exp(-C_Gmm1(2).*t) + C_Gmm2(1).*t.*exp(-C_Gmm2(2).*t);
term_1=@(x) 2.1e-6 + 2.433093685001734e+06.*x;
fplot(@(x) f_x(x),[0 5.*size],'b');
options_con = optimoptions('fmincon','Algorithm','interior-point','Display','iter-detailed','OptimalityTolerance', 1e-26,'ConstraintTolerance', 1e-7, 'StepTolerance', 1e-34, 'FunctionTolerance',1e-15,'MaxFunctionEvaluations', 1e10, 'MaxIterations', 1e11);