I am not currently unfamiliar with a numerical optimization, so I am studying them. What I am wondering is that I'd like to optimize a certain function with the following constraints by using gradient descent algorithm.
\begin{align} & \min\limits_{x}f(x) \\ & \text{subject to }\sum_{i} x_{i}=1 \quad \text{and} \quad x_{i} \geq 0 \end{align}
where the function $f$ is non-convex function. Is there any method to do optimization efficiently?
You can transform it to a Lagrangian function and minimize this function with the algorithm. Or find the first and/or second derivative and go for bisection or newton methods.