Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the convergence properties of a general inertial first-order proximal splitting algorithm for solving nonconvex nonsmooth optimization problems. Using the Kurdyka--\L ojaziewicz (KL) inequality  establish new convergence rates which apply to several inertial algorithms in the literature. Our basic assumption is that the objective function is semialgebraic, which lends our results broad applicability in the fields of signal processing and machine learning. The convergence rates depend on the exponent of the "desingularizing function" arising in the KL inequality. Depending on this exponent, convergence may be finite, linear, or sublinear and of the form $O(k^{-p})$ for $p>1$.
['Patrick R. Johnstone', 'Pierre Moulin']
I am writing a research paper on a idea Convergence Rates of Inertial Splitting Schemes for Nonconvex Composite Optimization
[{"from": "human", "value": "I am writing a research paper on a idea Convergence Rates of Inertial Splitting Schemes for Nonconvex Composite Optimization"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the convergence properties of a general inertial first-order proximal splitting algorithm for solving nonconvex nonsmooth optimization problems. Using the Kurdyka--\\L ojaziewicz (KL) inequality  establish new convergence rates which apply to several inertial algorithms in the literature. Our basic assumption is that the objective function is semialgebraic, which lends our results broad applicability in the fields of signal processing and machine learning. The convergence rates depend on the exponent of the \"desingularizing function\" arising in the KL inequality. Depending on this exponent, convergence may be finite, linear, or sublinear and of the form $O(k^{-p})$ for $p>1$."}]