Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Using a geometric argument,  show that under a reasonable continuity condition, the Clarke subdifferential of a semi-algebraic (or more generally stratifiable) directionally Lipschitzian function admits a simple form: The normal cone to the domain and limits of gradients generate the entire Clarke subdifferential. The characterization formula  obtain unifies various apparently disparate results that have appeared in the literature. Our techniques also yield a simplified proof that closed semialgebraic functions on Rn have a limiting subdifferential graph of uniform local dimension n.
['Dmitriy Drusvyatskiy', 'Alexander Ioffe', 'Adrian S. Lewis']
I am writing a research paper on a idea Clarke Subgradients for Directionally Lipschitzian Stratifiable Functions
[{"from": "human", "value": "I am writing a research paper on a idea Clarke Subgradients for Directionally Lipschitzian Stratifiable Functions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Using a geometric argument,  show that under a reasonable continuity condition, the Clarke subdifferential of a semi-algebraic (or more generally stratifiable) directionally Lipschitzian function admits a simple form: The normal cone to the domain and limits of gradients generate the entire Clarke subdifferential. The characterization formula  obtain unifies various apparently disparate results that have appeared in the literature. Our techniques also yield a simplified proof that closed semialgebraic functions on Rn have a limiting subdifferential graph of uniform local dimension n."}]