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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', > 'activeset','Display','iterdetailed','TolX',1e10,'TolFun',1e15,'TolCon',1e20,'MaxFunEval',10000,'MaxIter',1000000,'DiffMinChange',1e15 > ); > 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).^2p(2).^2p(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/writingobjectivefunctions.html#brhkghv5
Also, your options settings are not very good. In particular, setting TolCon to 1e20 is the same as setting it to zero, which can cause problems for fmincon. And setting DiffMinChange to 1e15 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/tolerancesandstoppingcriteria.html
Good luck,
Alan Weiss MATLAB mathematical toolbox documentation



