Fincon Warning: undesired gradient requirement

Hi,

I'm having a problem using Fmincon and I cannot find a solution online. I have to minimize a function ('ikSolver' in the code below) whose input is a [10x1] vector of doubles:

%Get lower and upper boundaries
[lb,ub] = getLegJointLimits('A')
% Random starting point initialization
  rng('shuffle'); 
  qlegs = rand(10,1);
  % Boundaries on the parameters must be satified by 
  % the initial value in the optimization procedure thus:
  qlegs = lb + (ub-lb).*qlegs;

        options = optimset('Display','iter','MaxFunEvals',50000,...
                       'TolFun',1e-06,...
                       'MaxIter',50000,'LargeScale','on');

                [fqs,Fval,EXITFLAG] = fmincon('ikSolver',qlegs,[],[],[],[],lb,ub,'constraint',options);

The values of the boundary vectors are:

lb =
   -0.6685
   -0.9745
    0.1193
   -1.5464
   -0.6229
   -0.2624
   -1.5480
    0.1282
   -0.9782
   -0.2811
ub =
    0.2712
    0.7202
    1.8977
    0.2598
    0.3003
    0.6735
    0.2582
    1.8921
    0.7114
    0.6523

and the functions appearing (simplified for simplicity):

function F = ikSolver(theta)
  global Rmatr   % Relabeling matrix

    global gt gteq
    global H

    Qplus = Rmatr*theta;

    F = sum(Qplus)^2; 
    gt = [ ];
    gteq = [ ];

end

with:

Rmatr =

     0     0     0     0     0     0     0     0     0     1
     0     1     1     1     0     0    -1    -1     0     0
     0     0     0     0     0     0     0     1     0     0
     0     0     0     0     0     0     1     0     0     0
     0     0     0     0     0     1     0     0     0     0
     0     0     0     0     1     0     0     0     0     0
     0     0     0     1     0     0     0     0     0     0
     0     0     1     0     0     0     0     0     0     0
     0     1     0     0     0     0     0     0     0     0
     1     0     0     0     0     0     0     0     0     0

And 'constraint':

function [gtr,gteqr] = constraint(Jsolcons)
    global gt gteq

      gtr = gt;         %non linear inequality constraints
      gteqr = gteq;     %non linear equality constraints

return

The warning is the following:

Warning: To use the default trust-region-reflective algorithm you must supply the gradient in the objective function and set the GradObj option to 'on'. FMINCON will use the active-set algorithm instead. For information on applicable algorithms, see Choosing the Algorithm in the documentation. > In fmincon at 492

The same warning (and consequent wrong result) appears if I change the arguments of the function fmincon as for example:

[fqs,Fval,EXITFLAG] = fmincon('ikSolver',qlegs,[],[],[],[],lb,ub);
[fqs,Fval,EXITFLAG] = fmincon('ikSolver',qlegs,eye(10),ub);
options = optimset('Display','off','MaxFunEvals',50000,...
                     'TolFun',1e-06,...
                     'MaxIter',50000);

I don't understand where am I asking for the trust-region-reflective algorithm which requires the gradient...

Thank you very much!!

[Matt J]

Are you sure you really meant

    F = sum(Qplus.^2);

If you really did mean,

    F=sum(Qplus)^2

then your objective function is equivalent to

 Rsum=sum(Rmatr,1);

 F=(dot(Rsum,theta))^2;

Obviously it is then more efficient to pre-compute Rsum once rather thatnto repeatedly perform the more expensive matrix multiplication Rmatr*theta in every iteration of the algorithm.

Answer 1

[Kye Taylor]

The trust-region-reflective algorithm is the default option for fmincon.

You can specify the solver by adding the name-value pair

'Algorithm','active-set' to the input to optimset, as in the command

options = optimset('Display','off','MaxFunEvals',50000,...
                     'TolFun',1e-06,...
                     'MaxIter',50000,...
                     'Algorithm','active-set');

See the online doc at http://www.mathworks.com/help/optim/ug/choosing-a-solver.html#bsbqd7i for more info.

[Matilde]

Thank you that solved the problem. I don't know how in the past few months I was using fmincon like that without specifing the gradient and it always worked...

Answer 2

[Matt J]

Instead of using an alternative algorithm that doesn't require the gradient of the objective function, why not just supply the trust-region-reflective algorithm the gradient that it requires? The gradient in your case has a very simple form

gradient = 2*(Rmatr.'*Qplus)

I assume here that you really meant to write

F = sum(Qplus.^2);

as per my comment above.

[Matilde]

Thank you very much for your advice, actually as I tried to say not very clearly, my ikSolver is much more complex and it solves totally another kind of problem, I thought there was no point in coping it here without explaining its meaning :-) For this reason I put that stupid example! I'm not able to define a gradient for my obj function by hand since is a bit too complex!