How to use the gradient with respect to a given vector?

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Zac Minson 2021-12-13

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https://ww2.mathworks.cn/matlabcentral/answers/1610205-how-to-use-the-gradient-with-respect-to-a-given-vector

编辑： Zac Minson 2021-12-14

I am trying to implement an algorithm that uses the matrices R - ( m x m matrix) and K - ( n x n ) that are the inputs of a function f(R,K). I am trying to use a starting point z = [r,n] where r is the vectorization of R and n is the vectorization of K. Starting values of R and K are given thus z is also known. I need to calculate r(z) = [gradient_r(f(R,K)) gradient_n(f(R,K))].

Once this is calculated I will do more calculations and use my next starting point in the algorithm, so z is trying to optimize to r(z) = 0 which is the Kurush-Khan-Tucker condition. Thus optimizing my matrices R and K in the process.

I do not know whether I should use numerical or symbolic gradient or even if what I am trying to do is possible. The paper I am referencing appears to use this method.

I have been trying something like this:

syms z [48 1]
r = z([1:16]);
n = z([17:48]);
R_hat = Dr*r;
R = reshape(R_hat, [4,4]);
K_hat = Dn*n;
K = reshape(K_hat, [8,8]) + eye(8);
g = solve(gradient(ft_RK));