Updating constraints in Fmincon: clarification

Dear all,

May you please help me with this! I want to to update pr, Aeq and beq for every iteration. Every step, Fmincon has new Aeq and beq. All Aeq and beq are independent of each other! For example, I have two Aeq(s) and two beq(s) as the attached file and I want to run the code with N=2. 1st iteration, Fmincon solves for p using Aeq1, beq1 and pr. 2nd iteration, Fmincon solves for a new p using Aeq2, beq2 and pr=p (p solved from 1st iteration).Thanks a lot for your help!!!

Dat

function [p, fval] = MC_NT_try33(p0, Aeq, beq, N, opts)
  if nargin < 5
        opts = optimoptions('fmincon', 'Algorithm', 'interior-point', ...
                            'GradObj', 'on', 'DerivativeCheck', 'on');
  end
    M = length(p0);
    p = nan(N,M);
    fval = nan(N,1);
    lb = zeros(1,64);
    ub = ones(1,64);
    pr1=[0.2  0.442  0.0001  0.0001  0.343  0.0001  1.000
  1.000  0.0001  0.536  0.0001  0.0001  0.455  0.021  0.0001  0.0001];
    pr = horzcat(pr1, (1/3) * ones(1, 64-16));
    p0 = p0(:);
    pr = pr(:);

      for i=1:N
         [pr, fval(i)] = fmincon(@(p) fun(p, pr), p0, [], [],...
                                  Aeq, beq, lb, ub, [], opts);
         p(i,:) = pr;
      end
  end
  function [f, gradf] = fun(p, pr)
      %%objective function
      f = sum( p .* log(p) - p .* log(pr) );
      %%gradient of objective function
      if nargout > 1
        gradf = log(p) + 1 - log(pr);
      end
    end

[Matt J]

The question seems to have changed very little since the last 2 times you posted it. What exactly is new here, if I may ask?

[Dat Tran]

Every step, new Aeq and beq have to be inputted. Aeq and beq are independent of each other! For example, I have two Aeq and two beq as the attached file and I want to run the code with N=2. 1st iteration, Fmincon solves for p using Aeq1, beq1 and pr. 2nd iteration, Fmincon solves for a new p using Aeq2, beq2 and pr=p (p solved from 1st iteration).Thanks a lot for your help!!!

Answer 1

[Walter Roberson]

 function [p, fval] = MC_NT_try33(p0, Aeq, beq, N, opts)
  if nargin < 5
        opts = optimoptions('fmincon', 'Algorithm', 'interior-point', ...
                            'GradObj', 'on', 'DerivativeCheck', 'on');
  end
    M = length(p0);
    p = nan(N,M);
    fval = nan(N,1);
    lb = zeros(1,64);
    ub = ones(1,64);
    pr1=[0.2  0.442  0.0001  0.0001  0.343  0.0001  1.000
  1.000  0.0001  0.536  0.0001  0.0001  0.455  0.021  0.0001  0.0001];
    pr = horzcat(pr1, (1/3) * ones(1, 64-16));
    p0 = p0(:);
    pr = pr(:);

      for i=1:N
         [pr, fval(i)] = fmincon(@(p) fun(p, pr), p0, [], [],...
                                  Aeq, beq, lb, ub, [], opts);
         p(i,:) = pr;

         %now update your pr, Aeq, beq in some way
         pr = pr + randn(size(pr)) / 1000;
         Aeq = Aeq + randn(size(Aeq)) / 10000;
         beq = beq + randn(size(beq)) / 10000;
         %these changed values will be used in the next iteration of fmincon
      end
  end

function [f, gradf] = fun(p, pr)
    %%objective function
    f = sum( p .* log(p) - p .* log(pr) );
    %%gradient of objective function
    if nargout > 1
      gradf = log(p) + 1 - log(pr);
    end
  end

If adding random values to pr, Aeq, beq was not what you had in mind for "updating" pr, Aeq and beq for every iteration, then you should have been more specific.

[Dat Tran]

Thank you so much!

I have series of Aeq and beq from Excel file. How I can input and make the program "updating" for every iteration! (I know how to import data from excel but do not know how to make the program understand that I want to update Aeq and beq for every iteration).

Thanks alot!!!

[Walter Roberson]

We went over this before. Store the individual possibilities in cell arrays. Pass them in to the routine. Index them in the fmincon call.

[pr, fval(i)] = fmincon(@(p) fun(p, pr), p0, [], [],...
                                Aeq{i}, beq{i}, lb, ub, [], opts);

[Dat Tran]

Dear Roberson,

Thank so-oo much for helping me on this!!! I just understood your instruction :) Best, Dat