Convert a symbolic function in to optimization function

Hello dear Matlab Community,

I need to convert the following code automatically in the new form in order to optimize it automatically. This needs be done a couple of hundret times so there is no chance of doing it manually.

This is the symbolic function:

M1=10*sin(x1)*sin(x2) - 2*cos(x1)*sin(x2) - 12*cos(x2) - 3

This is how i would need in in order to work:

M1=@(x)10*sin(x(1))*sin(x(2)) - 2*cos(x(1))*sin(x(2)) - 12*cos(x(2)) - 3

Thank you for your help.

Greetings Richie

Answer 1

[Dyuman Joshi]

(Assuming you already have the symbolic toolbox) Use matlabFunction -

syms x1 x2

%Original symbolic expression
M1=10*sin(x1)*sin(x2) - 2*cos(x1)*sin(x2) - 12*cos(x2) - 3

M1 = 

%Converting the symbolic expression to a function handle 
M2 = matlabFunction(M1,"Vars",{symvar(M1)})

M2 = function_handle with value:
    @(in1)cos(in1(:,2)).*-1.2e+1-cos(in1(:,1)).*sin(in1(:,2)).*2.0+sin(in1(:,1)).*sin(in1(:,2)).*1.0e+1-3.0

Testing on some values -

%#1
val = [0 pi/2];
subs(M1,[x1 x2],val)

ans = 

M2(val)

ans = -5.0000

%#2
val = [pi pi];
subs(M1,[x1 x2],val)

ans = 

9

M2(val)

ans = 9

%#3
val = rand(1,2);
double(subs(M1,[x1 x2],val))

ans = -13.7025

M2(val)

ans = -13.7025

[Richard]

Thank you for your fast help, but if i want to insert in in the opimization function it doesnt work.

anonrosen = @(x)(100*(x(2) - x(1)^2)^2 + (1-x(1))^2);
opts = optimoptions(@fmincon,Algorithm="interior-point");
rng default % For reproducibility
problem = createOptimProblem("fmincon",...
    x0=randn(2,1),...
    objective=anonrosen,...
    lb=[-2;-2],...
    ub=[2;2],...
    options=opts);

gs = GlobalSearch;
[x,fval2] = run(gs,problem) 

The function needs to be replaced with the following part in the first line

@(x)(100*(x(2) - x(1)^2)^2 + (1-x(1))^2)

But if i replace it with your code it doesnt work, but if i write it manually it does

[Bruno Luong]

syms x1 x2
%Original symbolic expression
M1 = 10*sin(x1)*sin(x2) - 2*cos(x1)*sin(x2) - 12*cos(x2) - 3;
%Converting the symbolic expression to a function handle 
M2 = matlabFunction(M1,"Vars",{symvar(M1)});

M3 = @(x) M2(transpose(x));

opts = optimoptions(@fmincon,Algorithm="interior-point");
rng default % For reproducibility
problem = createOptimProblem("fmincon",...
    x0=randn(2,1),...
    objective=M3,...
    lb=[-2;-2],...
    ub=[2;2],...
    options=opts);
gs = GlobalSearch;
[x,fval2] = run(gs,problem) 

GlobalSearch stopped because it analyzed all the trial points.

All 9 local solver runs converged with a positive local solver exit flag.

x = 2×1

-1.3734 0.7044

fval2 = -18.7480

[Dyuman Joshi]

You need to supply a row vector, see my comments below

syms x1 x2

in = 100*(x2 - x1^2)^2 + (1-x1)^2;

out = matlabFunction(in,"Vars",{symvar(in)});

%anonrosen = @(x)(100*(x(2) - x(1)^2)^2 + (1-x(1))^2);

opts = optimoptions(@fmincon,Algorithm="interior-point");

rng default
problem = createOptimProblem("fmincon",...

%%corrected to give a row vector as an input

    x0=randn(1,2),...    

%%objective is the output of the conversion from symbolic

    objective=out,...
    lb=[-2;-2],...
    ub=[2;2],...
    options=opts);

gs = GlobalSearch;
[x,fval2] = run(gs,problem) 

GlobalSearch stopped because it analyzed all the trial points.

All 16 local solver runs converged with a positive local solver exit flag.

x = 1×2

1.0000 1.0000

fval2 = 2.1093e-11

[Richard]

Thank you for answers, it really helped me alot,

without you guys I wouldnt know what to do.

Have a nice day:)