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Generate Code for`quadprog`

First Steps in`quadprog`Code Generation

This example shows how to generate code for thequadprogoptimization solver. Code generation requires aMATLAB^®Coder™license. For details about code generation requirements, seeCode Generation for quadprog Background.

The problem is to minimize the quadratic expression

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

where

$H = [\begin{matrix} 1 & - 1 & 1 \\ - 1 & 2 & - 2 \\ 1 & - 2 & 4 \end{matrix}]$

and

$f = [\begin{matrix} 2 \\ - 3 \\ 1 \end{matrix}]$

subject to the constraints $0 \leq x \leq 1$ , $\sum x = 1 / 2$ .

Create a file namedtest_quadp.mcontaining the following code.

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'); [x,fval] = quadprog(H,f,[],[],Aeq,beq,lb,ub,x0,opts)

Generate code for thetest_quadpfile.

codegen-config:mextest_quadp

After some time,codegencreates a MEX file namedtest_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 topicOptimization 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.DynamicMemoryAllocation ='Off';

Create a file namedtest_quadp2.mcontaining the following code. This code sets a looser optimality tolerance than the default1e-8.

function[x, fval eflag、输出]= 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',...'OptimalityTolerance',1e-5); [x,fval,eflag,output] = quadprog(H,f,[],[],Aeq,beq,lb,ub,x0,opts)

Generate code for thetest_quadp2file.

codegen-configcfgtest_quadp2

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','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, runtest_quadp3在MATLAB生成代码。

[x,fval,exitflag,output] = test_quadp3

Solver stopped prematurely. quadprog stopped because it exceeded the iteration limit, options.MaxIterations = 2.000000e+00. x = -0.0000 0.5000 0 fval = -1.2500 exitflag = 0 output = struct with fields: algorithm: 'active-set' iterations: 2 constrviolation: 1.6441e-18 firstorderopt: 2 message: '↵Solver stopped prematurely.↵↵quadprog stopped because it exceeded the iteration limit,↵options.MaxIterations = 2.000000e+00.↵↵' linearsolver: [] cgiterations: []

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.