Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  notice that the results for the existence of global (local) saddle points of augmented Lagrangian functions in the literature re only sufficient conditions of some special types of augmented Lagrangian. ,  introduce a general class of nonlinear augmented Lagrangian functions for constrained optimization problem. In two different cases,  present sufficient and necessary conditions for the existence of global saddle points. Moreover, as corollaries of the two results above,  not only obtain sufficient and necessary conditions for the existence of global saddle points of some special types of augmented Lagrangian functions mentioned in the literature, but also give some aker sufficient conditions than the ones in the literature. Compared with our recent work (Wang et al. in Math Oper Res 38:740–760, 2013), the nonlinear augmented Lagrangian functions in this paper are more general and the results in this paper are original.  show that some examples (such as improved barrier augmented Lagrangian) satisfy the assumptions of this paper, but not available in Wang et al. (2013).
['Changyu Wang', 'Qian Liu', 'Biao Qu']
I am writing a research paper on a idea Global saddle points of nonlinear augmented Lagrangian functions
[{"from": "human", "value": "I am writing a research paper on a idea Global saddle points of nonlinear augmented Lagrangian functions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  notice that the results for the existence of global (local) saddle points of augmented Lagrangian functions in the literature re only sufficient conditions of some special types of augmented Lagrangian. ,  introduce a general class of nonlinear augmented Lagrangian functions for constrained optimization problem. In two different cases,  present sufficient and necessary conditions for the existence of global saddle points. Moreover, as corollaries of the two results above,  not only obtain sufficient and necessary conditions for the existence of global saddle points of some special types of augmented Lagrangian functions mentioned in the literature, but also give some aker sufficient conditions than the ones in the literature. Compared with our recent work (Wang et al. in Math Oper Res 38:740\u2013760, 2013), the nonlinear augmented Lagrangian functions in this paper are more general and the results in this paper are original.  show that some examples (such as improved barrier augmented Lagrangian) satisfy the assumptions of this paper, but not available in Wang et al. (2013)."}]