Initial values for fmincon

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.

[Rik]

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]

You might want to look at Global Optimization Toolbox's MultiStart()

[Ayesha Maroof]

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]

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