Vectorize quadcon in matlab for many cones

回答済み

Zohar Levi

2026年02月04日 19:44

I have a socp with millions of cones.

It seems that currently, it's only possible to add a quadcon one-by-one in a loop. This is effective only for small problems:

Moreover, a formulation of a cone must be as a quad cone, which requires to multiply the cone matrix by its transpose. This is inefficient programmatically and numerically.

Nothing has been seemed to improve in the past 7 years:
https://support.gurobi.com/hc/en-us/community/posts/360048464832-How-to-effectively-implement-quadratic-constraints-over-80-000

関連

• MATLAB
• SOCP

0

• 

  Riley Clement

  • Gurobi Staff

  2026年02月06日 06:46

  Hi Zohar,

  Adding multiple quadratic constraints in a single API call is not a feature in any of our APIs.  Can you point to an example in another solver API that demonstrates the functionality you are after?

  Moreover, a formulation of a cone must be as a quad cone, which requires to multiply the cone matrix by its transpose. This is inefficient programmatically and numerically.

  This can be avoided, as mentioned in my response to your other post.

  - Riley

  0
• 

  Zohar Levi

  2026年02月06日 22:05

  Mosek, e.g. (untested):

  clear prob;
  
  K = 4;          % number of cones
  d = 2;          % dimension of x inside each cone (so cone size = d+1 = 3)
  n = K*(d+1);    % total variables
  
  % Objective: minimize sum of all t_k
  c = zeros(n,1);
  c(1:(d+1):n) = 1;   % every (d+1)-th variable is a t_k
  
  prob.c   = c;
  prob.a   = sparse([]);   % no linear constraints
  prob.blc = [];
  prob.buc = [];
  
  prob.blx = -inf(n,1);
  prob.bux =  inf(n,1);
  
  % ----- Build cones -----
  % Each cone uses variables:
  %   cone k → indices (k-1)*(d+1) + [1, 2, ..., d+1]
  
  prob.cones.type   = repmat(mosek.ct.quad, 1, K);
  prob.cones.subptr = 1:(d+1):((d+1)*K);
  
  sub = zeros(1, n);
  for k = 1:K
      base = (k-1)*(d+1);
      sub(base+1 : base+(d+1)) = base+1 : base+(d+1);
  end
  prob.cones.sub = sub;
  
  % ----- Solve -----
  [r,res] = mosekopt('minimize', prob);
  
  

  Yalmip supports it as well, but the gurobi implementation is a slow loop.

  (Yeah, I mentioned the numerical issue twice for some reason.)

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• 

  Robert Luce

  • Gurobi Staff

  2026年02月13日 13:36

  It seems that currently, it's only possible to add a quadcon one-by-one in a loop. This is effective only for small problems

  What is the time you'd need to call it effective?  Here is a simple experiment I did: Create problem with 100.000 quadratic constraints each comprising 100 variables, creating the data one-by-one in a Matlab for loop:

  function qcp()                                                                                                                                                                                    
                                                                                                                                                                                                    
  t_start = tic();                                                                                                                                                                                  
                                                                                                                                                                                                    
  % Number of quadratic constraints                                                                                                                                                                 
  q = 100000;                                                                                                                                                                                        
                                                                                                                                                                                                    
  % Number of variables                                                                                                                                                                             
  n = 100000;                                                                                                                                                                                        
                                                                                                                                                                                                    
  % Number of variables participating in each quadratic constraint                                                                                                                                  
  qclen = 100;                                                                                                                                                                                      
                                                                                                                                                                                                    
  model.A = sparse(0, n);                                                                                                                                                                           
                                                                                                                                                                                                    
  for k = 1:q                                                                                                                                                                                       
      model.quadcon(k).Qrow = 1:qclen;                                                                                                                                                              
      model.quadcon(k).Qcol = 1:qclen;                                                                                                                                                              
      model.quadcon(k).Qval = rand(1, qclen);                                                                                                                                                       
      model.quadcon(k).q = sparse(n, 1);                                                                                                                                                            
      model.quadcon(k).rhs = 1.0;                                                                                                                                                                   
  end                                                                                                                                                                                               
                                                                                                                                                                                                    
  fprintf('Matlab model building time %.2fsec.\n', toc(t_start));                                                                                                                                   
                                                                                                                                                                                                    
  params.timelimit = 0;                                                                                                                                                                             
  result = gurobi(model, params);                                                                                                                                                                   
                                                                                                                                                                                                    
  end

  With Matlab 2019a on a 5 year old AMD box I get

  Matlab model building time 1.08sec.

  Doesn't look too bad to me?  I'm sure you can adapt this pattern to host the indices for the cones in model.quadcon(k).Qrow and model.quadcon(k).Qcol and put the corresponding +1.0/-1.0 coefficients in the model.quadcon(k).Qval array.

  Good luck!

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• 

  Zohar Levi

  2026年02月14日 22:36

  From a closer look, indeed the quadcon wasn't the culprit.

  Thanks

  0

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