LOCAL SADDLE-POINTS AND CONVEXIFICATION FOR NONCONVEX OPTIMIZATION PROBLEMS

Recently, Li (Ref. 1) obtained a saddle-point result for a general cla ss of nonconvex optimization problems with inequality constraints, by using a transformation equivalent to taking the pth power of the objec tive function and the constraints, under several conditions. In this p aper, we show that, by an equivalent transformation, using the pth pow er of the constraints or using the pth power of the objective function and the constraints, the same result can be obtained under much weake r and reasonable conditions. Also, our results can be extended to the problem in which equality and inequality constraints are involved.