Code Generation for Optimization Basics

Generate Code for fmincon

This example shows how to generate code for the fmincon optimization solver. Code generation requires a MATLAB® Coder™ license. For details of code generation requirements, see Code Generation in fmincon Background.

The example uses the following simple objective function. To use this objective function in your own testing, copy the code to a file named rosenbrockwithgrad.m. Save the file on your MATLAB path.

function [f,g] = rosenbrockwithgrad(x)
% Calculate objective f
f = 100*(x(2) - x(1)^2)^2 + (1 - x(1))^2;

if nargout > 1 % gradient required
    g = [-400*(x(2) - x(1)^2)*x(1) - 2*(1 - x(1));
        200*(x(2) - x(1)^2)];
end
end

To generate code using the rosenbrockwithgrad objective function, create a file named test_rosen.m containing code that calls rosenbrockwithgrad. You must set options to use the "sqp" algorithm. To use the provided gradient of the objective function, set the SpecifyObjectiveGradient option to true. To verify the results in MATLAB using the same code as is generated, set the UseCodegenSolver option to true.

function [x,fval,exitflag,output] = test_rosen(x0,lb,ub)
opts = optimoptions("fmincon",...
    Algorithm="sqp",SpecifyObjectiveGradient=true,...
    UseCodegenSolver=true);
[x,fval,exitflag,output] = fmincon(@rosenbrockwithgrad,...
    x0,[],[],[],[],lb,ub,[],opts);
end

Test this code in MATLAB.

x0 = [-1 1];
lb = [-3 -3];
ub = [3 3];
[x,fval,exitflag,output] = test_rosen(x0,lb,ub)
Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.


x =

    1.0000    1.0000


fval =

   5.6989e-20


exitflag =

     1


output = 

  struct with fields:

         iterations: 13
          funcCount: 49
          algorithm: 'sqp'
    constrviolation: 0
           stepsize: 2.1608e-06
       lssteplength: 1
      firstorderopt: 8.9962e-09
            message: 'Local minimum found that satisfies the constraints.↵↵Optimization completed because the objective function is non-decreasing in ↵feasible directions, to within the value of the optimality tolerance,↵and constraints are satisfied to within the value of the constraint tolerance.'

Generate code for the test_rosen file.

codegen -config:mex test_rosen -args {x0,lb,ub}

After some time, codegen creates a MEX file named test_rosen_mex.mexw64 (the file extension will vary, depending on your system). You can run the resulting C code by entering

[x,fval] = test_rosen_mex(x0,lb,ub)

The results are the following or similar:

x =

    1.0000    1.0000


fval =

   5.6977e-20

The result using code generation is nearly the same as the result of running the code in MATLAB.

Modify Example for Efficiency

Following some of the suggestions in Optimization Code Generation for Real-Time Applications, set the configuration of the generated code to have fewer checks and to use static memory allocation.

cfg = coder.config("mex");
cfg.IntegrityChecks = false;
cfg.SaturateOnIntegerOverflow = false;
cfg.EnableDynamicMemoryAllocation = false;

First check the average time to run the problem using generated code with the default mex code generation options.

N = 10000; % Run 10,000 trials
pp = zeros(N,1);
for i=1:N
    tic
    [x,fval,exitflag,output] = test_rosen_mex(x0,lb,ub);
    pp(i) = toc;
end
m = mean(pp)
m =

   8.9106e-05

Generate code using the cfg configuration.

codegen -config cfg test_rosen -args {x0,lb,ub}

Check the average time to run the problem using generated code with the cfg configuration.

N = 10000; % Run 10,000 trials
pp = zeros(N,1);
for i=1:N
    tic
    [x,fval,exitflag,output] = test_rosen_mex(x0,lb,ub);
    pp(i) = toc;
end
m = mean(pp)
m =

   6.0810e-05

The average time to run the generated code is about 2/3 of the previous time.

Try limiting the number of allowed iterations to 20, which is about half of those taken in the first computation.

function [x,fval,exitflag,output] = test_rosen3(x0,lb,ub)
options = optimoptions("fmincon",...
    Algorithm="sqp",SpecifyObjectiveGradient=true,...
    UseCodegenSolver=true,MaxIterations=20);
[x,fval,exitflag,output] = fmincon(@rosenbrockwithgrad,...
    x0,[],[],[],[],lb,ub,[],options);
end

Run test_rosen3 in MATLAB.

[x,fval,exitflag,output] = test_rosen3(x0,lb2,ub2)
x =

    0.2852    0.0716


fval =

    0.5204


exitflag =

     0


output = 

  struct with fields:

         iterations: 20
          funcCount: 70
          algorithm: 'sqp'
    constrviolation: 0
           stepsize: 0.0225
       lssteplength: 1
      firstorderopt: 1.9507
            message: 'Solver stopped prematurely.↵↵fmincon stopped because it exceeded the iteration limit,↵options.MaxIterations = 2.000000e+01.'

With this severe iteration limit, fmincon does not reach a good solution. The tradeoff between accuracy and speed can be difficult to manage.

Generate Code for Single-Precision Computations

To generate code for single-precision data, the only change you need is to pass all data as single-precision.

x0 = single([-1 1]);
lb = single([-3 -3]);
ub = single([3 3]);
[x,fval] = test_rosen(x0,lb,ub)
Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.


x =

  1×2 single row vector

    1.0000    1.0001


fval =

  single

  9.6799e-10

The resulting fval is of the order 1e-10 rather than the double-precision result that is on the order of 1e-20, but other than that the procedure is identical.

Generate code and try the single-precision computation again.

codegen -config:mex test_rosen -args {x0,lb,ub}

Pass the single-precision input values to the generated function.

[x,fval] = test_rosen_mex(x0,lb,ub)
x =

  1×2 single row vector

    0.9999    0.9998


fval =

  single

  1.1349e-08

The generated code gives results that are close to the MATLAB results.

See Also

| (MATLAB Coder) |

Topics