Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  consider the least squares semidefinite programming with a large number of equality and inequality constraints. One difficulty in finding an efficient method for solving this problem is due to the presence of the inequality constraints. ,  propose to overcome this difficulty by reformulating the problem as a system of semismooth equations with two level metric projection operators.  then design an inexact smoothing Newton method to solve the resulting semismooth system. At each iteration,  use the BiCGStab iterative solver to obtain an approximate solution to the generated smoothing Newton linear system. Our numerical experiments confirm the high efficiency of the proposed method.
['Yan Gao', 'Defeng Sun']
I am writing a research paper on a idea Calibrating Least Squares Semidefinite Programming with Equality and Inequality Constraints
[{"from": "human", "value": "I am writing a research paper on a idea Calibrating Least Squares Semidefinite Programming with Equality and Inequality Constraints"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  consider the least squares semidefinite programming with a large number of equality and inequality constraints. One difficulty in finding an efficient method for solving this problem is due to the presence of the inequality constraints. ,  propose to overcome this difficulty by reformulating the problem as a system of semismooth equations with two level metric projection operators.  then design an inexact smoothing Newton method to solve the resulting semismooth system. At each iteration,  use the BiCGStab iterative solver to obtain an approximate solution to the generated smoothing Newton linear system. Our numerical experiments confirm the high efficiency of the proposed method."}]