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Topic: fmincon initial point problem
Replies: 2   Last Post: Mar 18, 2013 12:01 PM

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 Alan Weiss Posts: 1,430 Registered: 11/27/08
Re: fmincon initial point problem
Posted: Mar 18, 2013 10:52 AM

On 3/18/2013 10:08 AM, Haemish wrote:
> Dear sir,
>
> I have some questions on fmincon initial value problem.
>
> The code belows are very simple one which find the minimum value.
>
> That is finding x^2+y^2+z^2+75 when lb=[0 0 0] and ub=[5 5 5]
> with constraint of x+y+z=8
>
> I think that even such a simple problem depends on the initial value
> strongly.
>
> Initial point [0 0 0] gives the answer [2.667 2.667 2.667] but initial
> point [0 1 1] gives the answer [0 4 4]. However I know that the answer
> is [0 3 5] (irrespective the [x y z] sequence).
>
> I think that this is convex quadratic problem but fmincon minimization
> answer should be found uniquely.
> Are there any problems on my probelm definition? And are there any
> tips to overcome fmincon initial value problem except for random
> initial value startings?
>
> Sincerely yours
>
> Thank you.
>
> ----------------------------- code
> ----------------------------------------
> %main.m
> optNLP = optimset( 'UseParallel','always','Algorithm',
> 'active-set','Display','iter-detailed','TolX',1e-10,'TolFun',1e-15,'TolCon',1e-20,'MaxFunEval',10000,'MaxIter',1000000,'DiffMinChange',1e-15
> );
> pCOM0 = [0 5 5]';
> lb = [0*ones(3,1)]; ub =
> [5*ones(3,1)]; [popt, Jopt,
> exitflag,output,labda,grad,hessian] = fmincon( @(p)obj(p), pCOM0,[],
> [], [], [], lb, ub, @(p)ctr(p), optNLP)
>
> %ctr.m
> function [c,ceq] = ctr(p)
> ceq=sum(p)-8;
> c=[];
> end
>
> %obj.m
> function Y = obj(p)
> Y = -p(1).^2-p(2).^2-p(3).^2+75;
> end

You are finding a maximum, not a minimum, with your objective function.
That is the result when you take -sum(p.^2) as the objective instead of
sum(p.^2). See
http://www.mathworks.com/help/optim/ug/writing-objective-functions.html#brhkghv-5

Also, your options settings are not very good. In particular, setting
TolCon to 1e-20 is the same as setting it to zero, which can cause
problems for fmincon. And setting DiffMinChange to 1e-15 makes no sense
at all, leave it at the default value, and use centered finite
differences if you want more accuracy (set FinDiffType to 'centered'). See
http://www.mathworks.com/help/optim/ug/tolerances-and-stopping-criteria.html

Good luck,

Alan Weiss
MATLAB mathematical toolbox documentation

Date Subject Author
3/18/13 Alan Weiss
3/18/13 Matt J