Suppose that we want to find the solution(s) of the following system of equations: $$ g(x)_i=0 \ \ \ i=1,2,..m $$ , where $x \in R^n$ and $g(x)_i$ is any arbitrary differentiable function.
Can we instead try to solve the following optimization problem? $$ min\ \sum_i g(x)^2_i $$ And then, find $$ \sum_{i}2g({x}^{*})_{i}\nabla g({x}^{*})_i=0 $$ and check if $\sum_i g({x}^{*})^2_i$ equals zero?
If $\sum_i g(x)^2_i$ is strictly convex, can we also conclude that the system has at most one unique solution?