Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The feasibility problem for a system of linear inequalities can be converted into an unconstrained optimization problem by using ideas from the ellipsoid method, which can be vied as a very simple minimization technique for the resulting nonlinear function. This function is related to the volume of an ellipsoid containing all feasible solutions, which is parametrized by certain ights which  choose to minimize the function. The center of the resulting ellipsoid turns out to be a feasible solution to the inequalities. Using more sophisticated nonlinear minimization algorithms,  develop and investigate more efficient methods, which lead to two kinds of ighted centers for the feasible set. Using these centers,  develop new algorithms for solving linear programming problems.
['Aiping Liao', 'Michael J. Todd']
I am writing a research paper on a idea Solving LP Problems via Weighted Centers
[{"from": "human", "value": "I am writing a research paper on a idea Solving LP Problems via Weighted Centers"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The feasibility problem for a system of linear inequalities can be converted into an unconstrained optimization problem by using ideas from the ellipsoid method, which can be vied as a very simple minimization technique for the resulting nonlinear function. This function is related to the volume of an ellipsoid containing all feasible solutions, which is parametrized by certain ights which  choose to minimize the function. The center of the resulting ellipsoid turns out to be a feasible solution to the inequalities. Using more sophisticated nonlinear minimization algorithms,  develop and investigate more efficient methods, which lead to two kinds of ighted centers for the feasible set. Using these centers,  develop new algorithms for solving linear programming problems."}]