  This paper defines a strong convertible nonconvex(SCN) function for solving
the unconstrained optimization problems with the nonconvex or
nonsmooth(nondifferentiable) function. First, many examples of SCN function are
given, where the SCN functions are nonconvex or nonsmooth. Second, the
operational properties of the SCN functions are proved, including addition,
multiplication, compound operations and so on. Third, the SCN forms of some
special functions common in machine learning and engineering applications are
presented respectively where these SCN function optimization problems can be
transformed into minmax problems with a convex and concave objective function.
Fourth,a minmax optimization problem of SCN function and its penalty function
are defined. The optimization condition,exactness and stability of the minmax
optimization problem are proved. Finally, an algorithm of penalty function to
solve the minmax optimization problem and its convergence are given. This paper
provides an efficient technique for solving unconstrained nonconvex or
nonsmooth(nondifferentiable) optimization problems to avoid using
subdifferentiation or smoothing techniques.
