Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Finding low-rank solutions of semidefinite programs is important in many applications. For example, semidefinite programs that arise as relaxations of polynomial optimization problems are exact relaxations when the semidefinite program has a rank-1 solution. Unfortunately, computing a minimum-rank solution of a semidefinite program is an NP-hard problem.   review the theory of low-rank semidefinite programming, presenting theorems that guarantee the existence of a low-rank solution, heuristics for computing low-rank solutions, and algorithms for finding low-rank approximate solutions. Then  present applications of the theory to trust-region problems and signal processing.
['Alex Lemon', 'Anthony Man-Cho So', 'Yinyu Ye']
I am writing a research paper on a idea Low-Rank Semidefinite Programming: Theory and Applications
[{"from": "human", "value": "I am writing a research paper on a idea Low-Rank Semidefinite Programming: Theory and Applications"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Finding low-rank solutions of semidefinite programs is important in many applications. For example, semidefinite programs that arise as relaxations of polynomial optimization problems are exact relaxations when the semidefinite program has a rank-1 solution. Unfortunately, computing a minimum-rank solution of a semidefinite program is an NP-hard problem.   review the theory of low-rank semidefinite programming, presenting theorems that guarantee the existence of a low-rank solution, heuristics for computing low-rank solutions, and algorithms for finding low-rank approximate solutions. Then  present applications of the theory to trust-region problems and signal processing."}]