Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago, ADMM so far can be applied only to unconstrained problems and problems with linear equality or inequality constraints. Our extension can handle arbitrary inequality constraints directly. It combines the ability of ADMM to solve convex optimization problems in a distributed setting with the ability of the Augmented Lagrangian method to solve constrained optimization problems, and as  show, it inherits the convergence guarantees of ADMM and the Augmented Lagrangian method.
['Joachim Giesen', 'Sören Laue']
I am writing a research paper on a idea Distributed Convex Optimization with Many Convex Constraints
[{"from": "human", "value": "I am writing a research paper on a idea Distributed Convex Optimization with Many Convex Constraints"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago, ADMM so far can be applied only to unconstrained problems and problems with linear equality or inequality constraints. Our extension can handle arbitrary inequality constraints directly. It combines the ability of ADMM to solve convex optimization problems in a distributed setting with the ability of the Augmented Lagrangian method to solve constrained optimization problems, and as  show, it inherits the convergence guarantees of ADMM and the Augmented Lagrangian method."}]