Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a nonconvex constrained minimization problem,  introduce the dual problem by means of the ordinary Lagrangean function. The aim of the paper is to give, by means of the “image problem,” an estimate of the duality gap using the definition of lack of convexity of a function.
['M. Pappalardo']
I am writing a research paper on a idea On the duality gap in nonconvex optimization
[{"from": "human", "value": "I am writing a research paper on a idea On the duality gap in nonconvex optimization"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Given a nonconvex constrained minimization problem,  introduce the dual problem by means of the ordinary Lagrangean function. The aim of the paper is to give, by means of the \u201cimage problem,\u201d an estimate of the duality gap using the definition of lack of convexity of a function."}]