fmincon with 2 decision variables and multiple value of one parameter in the model

Hi, I am using fmincon to do the constrained optimisation problem with 2 decision variables. Furthermore, I have one variable which is not the decision variable in the model. I wish to check how the value of this variable has an impact on the 2 decision variables. See below in detail.

max m*x(1)+2*x(2)+x(1)*x(2)
s.t. x(1)+x(2)<=18
     x(1)>=0
     x(2)>=0

check m=2:0.2:3, the optimal solution of x(1) and x(2).

how can I write the range of m in the code.

Thanks

[Matt J]

Looks like QUADPROG would be more appropriate here than FMINCON.

Answer 1

[Shashank Prasanna]

You are doing a parameter sweep. Run fmincon in a loop for the specified m

for m=2:0.2:3

fmincon(@(x)obj(x,m),x0,.....)

end

Where obj(x,m) is your objective function. Since you are interested in maximizing make sure that you flip the sign since fmincon always minimizes.

[Ni]

Thanks Shashank for the reply. I use both command window and edit window.

May I kindly ask you to confirm my input

edit window

function f=myfun(x,m) f(1)=m*x(1); f(2)=2*x(2); f(3)=x(1)*x(2); f=f(1)+f(2)+f(3); f=-f;

command window

for m=2:0.2:3 [x,fval]=fmincon('myfun',x0,[1,1],18,[],[],[0;0],[Inf;Inf]) end

but, it is not working ....

Could you help accordingly; Thanks.

[Shashank Prasanna]

Hi Ni, can you use the code formatting button to format your code, its hard to read. It looks like this --> {}Code, and makes code look like this:

function f = mfun

[Shashank Prasanna]

f = @(x,m)(-m*x(1) + 2*x(2) + x(1)*x(2))

for m=2:0.2:3 

[x,fval]=fmincon(@(x)f(x,m),x0,[1,1],18,[],[],[0;0],[Inf;Inf]) 

end

If something doesn't work please provide info on why you think it doesn't work. This includes error messages, results or anything else that makes you believe that it doesn't work.

[Ni]

hi Shashank, unfortunately it is not working.

Error message provided as : error(message('optimlib:fmincon:WrongNumberOfColumnsInA', sizes.nVar))

do you have idea on this? Thanks.

[Ni]

hi Shashank, thanks, I run it again. It works. Thanks so much.

[Ni]

Hi Shashank,a quick question, do you know how I can plot with m and optimal solution of x(1). Thanks.

[Shashank Prasanna]

f = @(x,m)(-m*x(1) + 2*x(2) + x(1)*x(2))

m=2:0.2:3 

for ii = 1:length(m)

[x(:,ii),fval]=fmincon(@(x)f(x,m(ii)),x0,[1,1],18,[],[],[0;0],[Inf;Inf]) 

end

plot(m,x(1,:))