Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies the limiting behavior of ighted infeasible central paths for semidefinite programming obtained from centrality equations of the form X S+SX=2 ν W, where W is a fixed positive definite matrix and ν>0 is a parameter, under the assumption that the problem has a strictly complementary primal-dual optimal solution.  present a different and simpler proof than the one given by Preis and Stoer [Preis, M. and Stoer, J., 2004, Analysis of infeasible-interior-point paths arising with semidefinite linear complementarity problems. Mathematical Programming 99, 499-520.] that a ighted central path as a function of ν can be extended analytically beyond 0. In addition, the characterization of the limit points of the path and its normalized first-order derivatives is also provided.  also derive an error bound on the distance beten a point lying in a certain neighborhood of the central path and the set of primal-dual optimal solutions. Finally,  make some observation for the superlinear convergence of some primal-dual interior point SDP algorithms using AHO neighborhood.
['Zhaosong Lu', 'Renato D. C. Monteiro']
I am writing a research paper on a idea Limiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming
[{"from": "human", "value": "I am writing a research paper on a idea Limiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies the limiting behavior of ighted infeasible central paths for semidefinite programming obtained from centrality equations of the form X S+SX=2 \u03bd W, where W is a fixed positive definite matrix and \u03bd>0 is a parameter, under the assumption that the problem has a strictly complementary primal-dual optimal solution.  present a different and simpler proof than the one given by Preis and Stoer [Preis, M. and Stoer, J., 2004, Analysis of infeasible-interior-point paths arising with semidefinite linear complementarity problems. Mathematical Programming 99, 499-520.] that a ighted central path as a function of \u03bd can be extended analytically beyond 0. In addition, the characterization of the limit points of the path and its normalized first-order derivatives is also provided.  also derive an error bound on the distance beten a point lying in a certain neighborhood of the central path and the set of primal-dual optimal solutions. Finally,  make some observation for the superlinear convergence of some primal-dual interior point SDP algorithms using AHO neighborhood."}]