  Let $S\subset \mathbb{C}^n$ be a non-singular algebraic set and $f \colon
\mathbb{C}^n \to \mathbb{C}$ be a polynomial function. It is well-known that
the restriction $f|_S \colon S \to \mathbb{C}$ of $f$ on $S$ is a locally
trivial fibration outside a finite set $B(f|_S) \subset \mathbb{C}.$ In this
paper, we give an explicit description of a finite set $T_\infty(f|_S) \subset
\mathbb{C}$ such that $B(f|_S) \subset K_0(f|_S) \cup T_\infty(f|_S),$ where
$K_0(f|_S)$ denotes the set of critical values of the $f|_S.$ Furthermore,
$T_\infty(f|_S)$ is contained in the set of critical values of certain
polynomial functions provided that the $f|_S$ is Newton non-degenerate at
infinity. Using these facts, we show that if $\{f_t\}_{t \in [0, 1]}$ is a
family of polynomials such that the Newton polyhedron at infinity of $f_t$ is
independent of $t$ and the $f_t|_S$ is Newton non-degenerate at infinity, then
the global monodromies of the $f_t|_S$ are all isomorphic.
