How to define an objective function in the fmincon?
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I would like to solve a large scale non-convex QCQP problem using fmincon, such that
min_x x.'H*x
s.t. x.'*R*x = 1
Ax<=b
where H and R are positive definite matrices. Because x has dimension of 5000, how can i define the objective function? I tried to pass
obj = @(x)x.'*H*x;
to the fmincon, it won't work.
many thanks
1 Comment
Matt J
on 7 Dec 2021
There's nothing obviously incorrect in what you've described. You should attach a .mat file with your H,R,A,b matrices and demonstrate what you've done using the Run button
Answers (1)
Rik
on 7 Dec 2021
Your objective function should return a scalar. To borrow a term from machine learning: it is a cost function.
One of the often used functions to compute a single cost for a set of observations is the ordinary least squares:
OLS=@(x) sum((fun(x)-target).^2);
2 Comments
Rik
on 7 Dec 2021
If it already returns a scalar, what is your question?
From the documentation:
fun — Function to minimize
Function to minimize, specified as a function handle or function name. fun is a function that accepts a vector or array x and returns a real scalar f, the objective function evaluated at x.
fmincon passes x to your objective function and any nonlinear constraint functions in the shape of the x0 argument. For example, if x0 is a 5-by-3 array, then fmincon passes x to fun as a 5-by-3 array. However, fmincon multiplies linear constraint matrices A or Aeq with x after converting x to the column vector x(:).
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