I'm trying to replicate a paper. In the paper,there are several optimization problems. I wonder what kind of solver should be used in Matlab coding.
For example, one problem goes like this:
$$min \sum_{t=1}^T((\sum_{i=1}^{S}\delta^{-t}\pi_{ts}({\beta_0+\beta_1r_s+\beta_2r_s^2+\beta_3tr_s+\beta_4tr_s^2}))-1)^2$$
where $r_s,\pi_{ts},T,S$ is given. The goal of the optimaztion problem is to find $\beta$ and $\delta$. The constraints are: $$\beta_0>0$$ $$\delta\in(0,1]$$ ${\beta_0+\beta_1r_s+\beta_2r_s^2+\beta_3tr_s+\beta_4tr_s^2}>0$ for all $s\in(1,...,S)$ and $t\in(1,...,T)$ $$A\beta+B\delta>C$$ $A,B,C$ is a given matrix.
There is a function named "fmincon" which solves the non-linear optimization with non-linear constraints problems.