Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Nonconvex and nonsmooth optimization problems with linear equation and generalized orthogonality constraints have wide applications. These problems are difficult to solve due to nonsmooth objective function and nonconvex constraints. , by introducing an extended proximal alternating linearized minimization (EPALM) method,  propose a framework based on the augmented Lagrangian scheme (EPALMAL).  also show that the EPALMAL method has global convergence in the sense that every bounded sequence generated by the EPALMAL method has at least one convergent subsequence that converges to the Karush–Kuhn–Tucker point of the original problem. Experiments on a variety of applications, including compressed modes and multivariate data analysis, have demonstrated that the proposed method is noticeably efficient and achieves comparable performance with existing methods.
['Hong Zhu', 'Xiaowei Zhang', 'Delin Chu', 'Li-Zhi Liao']
I am writing a research paper on a idea Nonconvex and Nonsmooth Optimization with Generalized Orthogonality Constraints: An Approximate Augmented Lagrangian Method
[{"from": "human", "value": "I am writing a research paper on a idea Nonconvex and Nonsmooth Optimization with Generalized Orthogonality Constraints: An Approximate Augmented Lagrangian Method"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Nonconvex and nonsmooth optimization problems with linear equation and generalized orthogonality constraints have wide applications. These problems are difficult to solve due to nonsmooth objective function and nonconvex constraints. , by introducing an extended proximal alternating linearized minimization (EPALM) method,  propose a framework based on the augmented Lagrangian scheme (EPALMAL).  also show that the EPALMAL method has global convergence in the sense that every bounded sequence generated by the EPALMAL method has at least one convergent subsequence that converges to the Karush\u2013Kuhn\u2013Tucker point of the original problem. Experiments on a variety of applications, including compressed modes and multivariate data analysis, have demonstrated that the proposed method is noticeably efficient and achieves comparable performance with existing methods."}]