How to verify whether a solution to an optimization problem is correct. Consider a general optimization problem
min f(x)
subject to g(x) <=0
       h(x)=0,

where x denotes a vector and the functions are $R^n$ -> $R^n$.
suppose somebody gave me a solution x*, how can I verify whether this solution is correct?
One straight forward idea is to check whether x* satisfies the constrains. But how can I determine whether x* will minimize f(x)?

You could try and plot it (using some mathematics software) and see if the solution is actually a minimum within the constrains.
