How to write code for projected gradient descent?

clc;
clear;
a=0.01;
x=[0;0;0]
b=1
for i=1:1000
    if b<10^-6
        break
    end
    r=x-a*f(x)
    b=proj(r-x)
    x=r
end
display(x)

I want to write a code to find projected gradient descent of a function. (f(x) is gradient of a function, it is not the function itself)

I'm thinking about define a function proj(). But I don't understand how to write the argmin norm(x-y)^2 part

function f=proj(x)
...
end

Can you give me an example on how to write this code?

Answer 1

[Aditya Patil]

The min function in MATLAB optionally returns the index of the minimum value. You can calculate the function for all input values, and then use the minimum index to find which inputs are the argmin.

A = [1 9 -2; 8 4 -5]
[M,I] = min(A)