Initial values for fmincon

2018 12 21
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更新时间：2018 12 26
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I am trying to get the minimum value of a function using fmincon function but I have no guesses about the initial values.So what values should I provide at x0 so that it can be converged to minimum value? i am initiallly giving some values and also getting hessian matrix which is showing some positive and some negative numbers which is a proof that the obtained value is not minimum of function.

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Rik
Rik 2018-12-21
Good initial values depend strongly on your specific situation. Especially fminsearch (and probably fmincon as well) sometimes perform very badly if you have an initial guess that is far from a good solution.
Walter Roberson
Walter Roberson 2018-12-21
You might want to look at Global Optimization Toolbox's MultiStart()
Ayesha Maroof
Ayesha Maroof 2018-12-21
ok thank you let me look at it.Right now i am getting this :
"Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the default value of the function tolerance,
and constraints are satisfied to within the default value of the constraint tolerance."
Though it says the local minimum found but Hessian matrix which i am getting is having both positive and negative values.I want all values to be positive so that it proves that the obtained function has been minimized
hessian =
0.8272 -0.1404 -0.0622 0.7519 -1.6917 -0.3578 2.0148 -0.0462 -0.0961
-0.1404 0.0367 -0.0430 -0.1227 0.2787 0.0611 -0.3385 -0.0045 0.0089
-0.0622 -0.0430 0.2765 0.0881 -0.1224 0.0669 0.3099 0.0407 0.0354
0.7519 -0.1227 0.0881 2.2642 -3.9153 -0.7057 4.5789 0.2219 0.2032
-1.6917 0.2787 -0.1224 -3.9153 7.2666 1.3976 -8.6220 -0.0511 0.0025
-0.3578 0.0611 0.0669 -0.7057 1.3976 1.3033 -1.8609 0.0115 -0.0557
2.0148 -0.3385 0.3099 4.5789 -8.6220 -1.8609 11.6125 -0.0301 0.0617
-0.0462 -0.0045 0.0407 0.2219 -0.0511 0.0115 -0.0301 0.3722 0.3274
-0.0961 0.0089 0.0354 0.2032 0.0025 -0.0557 0.0617 0.3274 0.4120
Alan Weiss
Alan Weiss 2018-12-26
Just because some values are negative doesn't mean that the resulting Hessian isn't positive semidefinite. In fact, when I asked MATLAB to calculate the eigenvaljes of your matrix, it gave me
vals = eig(A)
vals =
0.0000
0.0034
0.0490
0.2203
0.4015
0.7076
0.9154
1.0405
21.0335
See, all positive.
HOWEVER, in general the returned values of the Hessian are NOT RELIABLE. See fmincon Hessian.
Alan Weiss
MATLAB mathematical toolbox documentation

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Matt J
Matt J
2018-12-26

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