Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of \({\mathcal {Q}}\)-stationarity (Benko and Gfrerer in Optimization 66(1):61–92, 2017).  demonstrate how \({\mathcal {Q}}_M\)-stationary solutions of the quadratic program can be obtained.  show that all limit points of the sequence of iterates generated by the basic SQP method are at least M-stationary and by some extension of the method  also guarantee the stronger property of \({\mathcal {Q}}_M\)-stationarity of the limit points.
['Matúš Benko', 'Helmut Gfrerer']
I am writing a research paper on a idea An SQP method for mathematical programs with vanishing constraints with strong convergence properties
[{"from": "human", "value": "I am writing a research paper on a idea An SQP method for mathematical programs with vanishing constraints with strong convergence properties"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of \\({\\mathcal {Q}}\\)-stationarity (Benko and Gfrerer in Optimization 66(1):61\u201392, 2017).  demonstrate how \\({\\mathcal {Q}}_M\\)-stationary solutions of the quadratic program can be obtained.  show that all limit points of the sequence of iterates generated by the basic SQP method are at least M-stationary and by some extension of the method  also guarantee the stronger property of \\({\\mathcal {Q}}_M\\)-stationarity of the limit points."}]