define an objective function with user defined number of variables in fminunc()

Suppose I want to define the following function in matlab which returns the output of fminunc(). The problem here is the number of variables depends on the user input. How do I define the objective function fun() such that it automatically adapts to the number of variables.

function xmin = problem(n)
    if n == 1
        fun = @(x) x^2+2*x+3;
        xmin = fminunc(fun,1);
    end
    if n == 2
        fun = @(x) x(1)^2+x(2)^2+2*(x(1)+x(2))+3;
        xmin = fminunc(fun,[1 0]);
    end
    if n == 3
        fun = @(x) x(1)^2+x(2)^2+x(3)^2+2*(x(1)+x(2)+x(3))+3;
        xmin = fminunc(fun,[1 0 0]);
    end
    % n is the number of variables for fun.
    % the list goes on. n==4, n==5,...
end

Answer 1

[Matt J]

The only way fminunc knows the number of variables is by looking at numel(x0) where x0 is the initial guess:

xmin = fminunc(fun,x0)

It doesn't look at fun in any way to determine that. So, your current code should be fine.

You could make your initial guess a function of n in some way. Looking at the pattern you have now, you could modify to the following, but it seems to me that the benefit is marginal.

function xmin = problem(n)

    x0=[1,zeros(1,n-1)];

    switch n
        case n=1
        fun = @(x) x^2+2*x+3;
        case n=2
        fun = @(x) x(1)^2+x(2)^2+2*(x(1)+x(2))+3;
        case n=3
        fun = @(x) x(1)^2+x(2)^2+x(3)^2+2*(x(1)+x(2)+x(3))+3;
    end
    
    xmin = fminunc(fun,x0);
    
end

[Shikun Nie]

I mean I want to write a single fun() such that it automatically adaptes to n variable. n can be any integer. It is not possible to list all of them out. Notice that the functions can be written into a matrix form as |x|^2+[2,2,...]*x+3

[Matt J]

function xmin = problem(n)

    x0=[1,zeros(1,n-1)];
    
    fun=@(x) sum(polyval([1,2,0],x)) + 3; %3 is not really necessary - constant shift does not affect xmin
    
    xmin = fminunc(fun,x0);
    
end

[Shikun Nie]

thanks for your answer. I think it solves my problem. I come out with this code to mimic the problem in my project. It is not the original code.

Answer 2

[Catalytic]

In the narrow case where your fun is always going to be an anonymous function of x, you could do this -

xmin=problem(  @(x) x(1)^2+x(2)^2+x(3)^2+2*(x(1)+x(2)+x(3))+3    )

x0 = 1×3

1 0 0

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xmin = 1×3

-1.0000 -1.0000 -1.0000

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function xmin = problem(fun)


    n=numel( unique(extract(func2str(fun)  ,  "x(" + digitsPattern+")")) );

    x0=[1,zeros(1,n-1)]

    xmin = fminunc(fun,x0  ,optimoptions('fminunc','Display','off') );
    
end

Answer 3

[Stephen23]

"How do I define the objective function fun() such that it automatically adapts to the number of variables."

fun = @(x) sum(x.^2)+2*sum(x)+3;