Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Convex optimization has become an essential technique in many different disciplines. ,  consider the primal-dual algorithm minimizing augmented models with linear constraints, where the objective function consists of two proper closed convex functions; one is the square of a norm and the other one is a gauge function being partly smooth relatively to an active manifold. Examples of this situation can be found in signal processing, optimization, statistics and machine learning literature.  present a unified framework to understand the local convergence behaviour of the primal-dual algorithm for these augmented models. This result explains some numerical results shown in the literature on local linear convergence of the algorithm.
['Tao Sun', 'Roberto Barrio', 'Hao Jiang', 'Lizhi Cheng']
I am writing a research paper on a idea Local Linear Convergence of a Primal-Dual Algorithm for the Augmented Convex Models
[{"from": "human", "value": "I am writing a research paper on a idea Local Linear Convergence of a Primal-Dual Algorithm for the Augmented Convex Models"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Convex optimization has become an essential technique in many different disciplines. ,  consider the primal-dual algorithm minimizing augmented models with linear constraints, where the objective function consists of two proper closed convex functions; one is the square of a norm and the other one is a gauge function being partly smooth relatively to an active manifold. Examples of this situation can be found in signal processing, optimization, statistics and machine learning literature.  present a unified framework to understand the local convergence behaviour of the primal-dual algorithm for these augmented models. This result explains some numerical results shown in the literature on local linear convergence of the algorithm."}]