# Different solutions of fmincon when changing x0

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Daniela Würmseer on 31 Mar 2022
Edited: Matt J on 26 Apr 2022
I wanted to ask if it is normal that fmincon can have different solutions with different x0?
I implement an Algoritjm by myself and use fmincon as follows:
options = optimoptions('fmincon','Display','iter','Algorithm','sqp');
x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options)

Torsten on 31 Mar 2022
Edited: Torsten on 31 Mar 2022
I wanted to ask if it is normal that fmincon can have different solutions with different x0?
There can be several reasons for fmincon to converge to different "solutions" dependent on the starting point. But - sure - the optimization algorithm implemented in "fmincon" tries to find local extrema. If a function has more than one or is ill-behaved, it depends on the starting point to which of the local extrema the algorithm converges.
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Matt J on 26 Apr 2022
Edited: Matt J on 26 Apr 2022
You can look at the function values at the two solutions to see if they are nearly the same. If so, then plainly you have multiple minima. Better still, given the two solutions x1 and x2,you could plot the 1D function
g(t)=fun(t*x1+(1-t)*x2) % t from -1 to 2
If the graph is very flat between t=0 and t=1 or is very bumpy, it is a likely sign that your graph has multiple local/global minima.

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