Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The most time-consuming part of the Karmarkar algorithm for linear programming is the projection of a vector onto the nullspace of a matrix that changes at each iteration.  present a variant of the Karmarkar algorithm that uses standard variable-metric techniques in an innovative way to approximate this projection. In limited tests, this modification greatly reduces the number of matrix factorizations needed for the solution of linear programming problems.
['John E. Dennis', 'A.M. Morshedi', 'Kathryn Tuner']
I am writing a research paper on a idea A variable-metric variant of the Karmarkar algorithm for linear programming
[{"from": "human", "value": "I am writing a research paper on a idea A variable-metric variant of the Karmarkar algorithm for linear programming"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The most time-consuming part of the Karmarkar algorithm for linear programming is the projection of a vector onto the nullspace of a matrix that changes at each iteration.  present a variant of the Karmarkar algorithm that uses standard variable-metric techniques in an innovative way to approximate this projection. In limited tests, this modification greatly reduces the number of matrix factorizations needed for the solution of linear programming problems."}]