Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Motivated principally by the low-rank matrix completion problem,  present an extension of the Frank--Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a new approach to generating “in-face” directions at each iteration, as ll as through new choice rules for selecting beten in-face and “regular” Frank--Wolfe steps. Our framework for generating in-face directions generalizes the notion of away steps introduced by Wolfe. In particular, the in-face directions always keep the next iterate within the minimal face containing the current iterate.  present computational guarantees for the new method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates.  apply the new method to the matrix completion problem, where low-dimensional faces correspond to low-rank matrices.  present computational results that demonstrate the effectiveness of our methodo...
['Robert M. Freund', 'Paul Grigas', 'Rahul Mazumder']
I am writing a research paper on a idea An Extended Frank-Wolfe Method with "In-Face" Directions, and its Application to Low-Rank Matrix Completion
[{"from": "human", "value": "I am writing a research paper on a idea An Extended Frank-Wolfe Method with \"In-Face\" Directions, and its Application to Low-Rank Matrix Completion"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Motivated principally by the low-rank matrix completion problem,  present an extension of the Frank--Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a new approach to generating \u201cin-face\u201d directions at each iteration, as ll as through new choice rules for selecting beten in-face and \u201cregular\u201d Frank--Wolfe steps. Our framework for generating in-face directions generalizes the notion of away steps introduced by Wolfe. In particular, the in-face directions always keep the next iterate within the minimal face containing the current iterate.  present computational guarantees for the new method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates.  apply the new method to the matrix completion problem, where low-dimensional faces correspond to low-rank matrices.  present computational results that demonstrate the effectiveness of our methodo..."}]