On the modulus of Lipschitz smoothness of log-sum-exp function

Key Points

• The modulus of Lipschitz smoothness of the log-sum-exp function is foundational in optimization theory.
• Key metric shows that the Lipschitz smoothness constant is linked to the gradient's behavior across convex functions.
• Analysis of smoothness properties facilitates improved algorithm design for optimization problems involving log-sum-exp functions.
• Understanding these properties may enable developing more efficient optimization algorithms in various applications.