Generate Code for quadprog

First Steps in quadprog Code Generation

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

The problem is to minimize the quadratic expression

$$\frac{1}{2}{x}^{T}Hx+f^{T}x$$

where

$H=\left[\begin{array}{ccc}1& -1& 1\\ -1& 2& -2\\ 1& -2& 4\end{array}\right]$

and

$$f=\left[\begin{array}{c}2\\ -3\\ 1\end{array}\right]$$

subject to the constraints $$0\le x\le 1$$, $${\displaystyle \sum x}=1/2$$.

Create a file named test_quadp.m containing code that creates the problem and constraints. The file must set options to use the "active-set" algorithm. Also, set the UseCodegenSolver option to true so you can verify the results in MATLAB using the same code as is generated.

function [x,fval] = test_quadp
H = [1,-1,1
    -1,2,-2
    1,-2,4];
f = [2;-3;1];
lb = zeros(3,1);
ub = ones(size(lb));
Aeq = ones(1,3);
beq = 1/2;
x0 = zeros(3,1);
opts = optimoptions("quadprog",...
    Algorithm="active-set",UseCodegenSolver=true);
[x,fval] = quadprog(H,f,[],[],Aeq,beq,lb,ub,x0,opts);
end

Generate code for the test_quadp file.

codegen -config:mex test_quadp

After some time, codegen creates a MEX file named test_quadp_mex.mexw64 (the file extension varies, depending on your system). Run the resulting C code.

[x,fval] = test_quadp_mex

x =

         0
    0.5000
         0


fval =

   -1.2500

Modify Example for Efficiency

Following some of the suggestions in the topic Optimization Code Generation for Real-Time Applications, configure 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 = "Off";

Create a file named test_quadp2.m containing the following code. This code sets a looser optimality tolerance than the default 1e-8.

function [x,fval,eflag,output] = test_quadp2
H = [1,-1,1
    -1,2,-2
    1,-2,4];
f = [2;-3;1];
lb = zeros(3,1);
ub = ones(size(lb));
Aeq = ones(1,3);
beq = 1/2;
x0 = zeros(3,1);
opts = optimoptions("quadprog",...
    Algorithm="active-set",UseCodegenSolver=true,...
    OptimalityTolerance=1e-5);
[x,fval,eflag,output] = quadprog(H,f,[],[],Aeq,beq,lb,ub,x0,opts);
end

Generate code for the test_quadp2 file.

codegen -config cfg test_quadp2

Code generation successful.

Run the resulting code.

[x,fval,eflag,output] = test_quadp2_mex

x =

         0
    0.5000
         0


fval =

   -1.2500


eflag =

     1


output = 

  struct with fields:

          algorithm: 'active-set'
      firstorderopt: 8.8818e-16
    constrviolation: 0
         iterations: 3

Changing the optimality tolerance does not affect the optimization process, because the 'active-set' algorithm does not check this tolerance until it reaches a point where it stops.

Create a third file that limits the number of allowed iterations to 2 to see the effect on the optimization process.

function [x,fval,exitflag,output] = test_quadp3
H = [1,-1,1
    -1,2,-2
    1,-2,4];
f = [2;-3;1];
lb = zeros(3,1);
ub = ones(size(lb));
Aeq = ones(1,3);
beq = 1/2;
x0 = zeros(3,1);
opts = optimoptions("quadprog",...
    Algorithm="active-set",UseCodegenSolver=true,...
    MaxIterations=2);
[x,fval,exitflag,output] = quadprog(H,f,[],[],Aeq,beq,lb,ub,x0,opts)

To see the effect of these settings on the solver, run test_quadp3 in MATLAB without generating code.

[x,fval,exitflag,output] = test_quadp3

Solver stopped prematurely.

quadprog stopped because it exceeded the iteration limit,
options.MaxIterations = 2.000000e+00.


x =

         0
    0.5000
   -0.0000


fval =

   -1.2500


exitflag =

     0


output = 

  struct with fields:

          algorithm: 'active-set'
      firstorderopt: 2.0000
    constrviolation: 1.1102e-16
         iterations: 2
            message: 'Solver stopped prematurely.↵↵quadprog stopped because it exceeded the iteration limit,↵options.MaxIterations = 2.000000e+00.'

In this case, the solver reached the solution in fewer steps than the default. Usually, though, limiting the number of iterations does not allow the solver to reach a correct solution.