Robustness with fminimax

Hello everyone,

I have to study robustness of my system, so my variables are uncertain and I have to add another variable to my objective function and it becomes:

original objective-function: myfun = @(x) sum (x(1:n)./polyval(p3,x(1:n)));

robust optimization : min max myfun = @(x) sum ([x(1:n) + r(1:n)]./polyval(p3,[x(1:n) + r(1:n)])); min for "x" and max for "r" .

"r" is the perturbation so it is very small,

my problem is non-convex and with non-linear constraints, and I solve the original problem with fmincon and it provides a good optimum.

For the robust optimization, I think that I can solve it by the fminimax, but I don't know how formulate it ??

Thanks,

Answer 1

[Sargondjani]

they way you present the problem now, you could just replace x(1:n) with y(1:n)=x(1:n) + r(1:n) in the orginal problem....

if instead you want to get solutions for every r then you could looop through r:

myfun=@(x,r)....
r=...

for ir=1:length(r)
     my_fun_ir=@(x)myfun(x,r(ir))
    %solve minimax where you store every solution as x(ir), for example
end

i hope this helps...

Answer 2

[Mouloud]

think you for your answer,

but, I want to solve the minimax problem for overall profile, the objective is to find a robust solution i.e:

when the "x" makes a small variation "r", r is smaller then 0.5 for example , the solution is robust.

so it is a global optimization and I have to take into account the perturbation "r" for al instant n=length(x)