Convexification and existence of a saddle point in a pth-power reformulation for nonconvex constrained optimization

It is well-known that saddle point criteria is a sufficient optimality cond ition for constrained optimization problems. Convexity is a basic requireme nt for the development of duality theory and saddle point optimality. In th is paper we show that, under some mild conditions, the local convexity of L agrangian function and hence the existence of a local saddle point pair can be ensured in an equivalent p-th power reformulation for a general class o f nonconvex constrained optimization problems. We further investigate the c onditions under which a global saddle point pair can be guaranteed to exist . These results expand considerably the class of optimization problems wher e a saddle point pair exists, thus enlarging the family of nonconvex proble ms to which the dual-search methods can be applied.