Matlab - Power operator in objective function

Awaiting user input

Livia Paiva

• May 19, 2022 18:29

Hi community,

For this simple example problem, I'm getting an error that says "Undefined operator '^' for input arguments of type 'optim.problemdef.OptimizationExpression'."

prob = optimproblem('ObjectiveSense','maximize');

x = optimvar('x');
y = optimvar('y', 'LowerBound', 1);
z = optimvar('z', 'LowerBound', 0);

prob.Objective = test_fun([x y z]);
prob.Constraints.cons1 = x + 2* y + 3 * z <= 4;
prob.Constraints.cons2 = x + y >= 1;

options = optimoptions('linprog');
sol = solve(prob, options);


function sol = test_fun(b)
    x = b(1);
    y = b(2);
    z = b(3);
    sol = x + y + 2 ^ z;
end

I'm using the Matlab's interface for Gurobi. How can I have design variable as an exponent in my objective function?

Thanks!

0

• 

  Jaromił Najman

  Gurobi Staff

  • May 20, 2022 11:32

  Hi Livia,

  To model the \(2^z\) function, you have to use Gurobi general constraint interface. In your particular case, you have to use the genconexpa struct array. There is no example showing exactly this function but the gc_pwl_func.m example shows the usage of the genconexp struct array, which works analogously.

  Best regards, 
  Jaromił

  0
• 

  Livia Paiva

  • May 20, 2022 19:20

  

  

  

  Hi Jaromil,

  Thanks for your reply! I'm trying to adapt my problem to the example you sent. But in my case, the objective function is not a linear combination of the design variables, it is a rather complex nonlinear function.

  In the example you sent me (simplified below), how can I change m.obj to be a function that has the design variables as arguments?

  % Four nonneg. variables x, y, u, v, one linear constraint u + 4*v <= 9
  m.varnames = {'x', 'y', 'u', 'v'};
  m.lb = zeros(4, 1);
  m.ub = +inf(4, 1);
  m.A = sparse([0, 0, 1, 4]);
  m.rhs = 9;
  
  % Objective
  m.modelsense = 'max';
  m.obj = [2; 1; 0; 0];
  
  % Set u \approx exp(x)
  m.genconexp.xvar = 1;
  m.genconexp.yvar = 3;
  m.genconexp.name = 'gcf1';
  
  % Set v \approx sqrt(y) = y^0.5
  m.genconpow.xvar = 2;
  m.genconpow.yvar = 4;
  m.genconpow.a = 0.5;
  m.genconpow.name = 'gcf2';
  
  % Parameters for discretization: use equal piece length with length = 1e-3
  params.FuncPieces = 1;
  params.FuncPieceLength = 1e-3;
  
  % Solve and print solution
  result = gurobi(m, params);
  printsol(result.objval, result.x(1), result.x(2), result.x(3), result.x(4));

  Thanks again!

  0
• 

  Jaromił Najman

  Gurobi Staff

  • May 30, 2022 07:05

  Hi Livia,

  I am not sure whether I understand your question. Your general constraints define the constraints \(u = \exp(x)\) and \(v = \sqrt{y}\). You can now use variables \(u\) and \(v\) to, e.g., add \(\exp(x)\) and \(\sqrt{y}\) in the objective by

  m.obj = [0; 0; 1; 1];

  Does this answer your question?

  Best regards, 
  Jaromił

  0

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