Existence of a saddle point in nonconvex constrained optimization

The existence of a saddle point in nonconvex constrained optimization probl ems is considered in this paper. We show that, under some mild conditions, the existence of a saddle point can be ensured in an equivalent p-th power formulation for a general class of nonconvex constrained optimization probl ems. This result expands considerably the class of optimization problems wh ere a saddle point exists and thus enlarges the family of nonconvex problem s that can be solved by dual-search methods.