Log-Sum-Exp (LSE) Function and PropertiesThe log-sum-exp (LSE) function in ![]()
The log-sum-exp function is increasing with respect to each argument, and convex. Proof: The monotonicity of the log-sum-exp function is obvious. The convexity is obtained as follows. As seen here, the Hessian of the log-sum-exp function is ![]() where We need to check that for every ![]() due to the Cauchy-Schwartz inequality. |