
Understanding the proof of: Every convex function is continuous
Aug 18, 2020 · Midpoint-Convex and Continuous Implies Convex 11 Prob. 23, Chap. 4, in Baby Rudin: Every convex function is continuous and every increasing convex function of a convex …
Proving a function of matrix is convex - Mathematics Stack Exchange
Feb 16, 2015 · Convexity is the exception, not the rule. In my experience, nearly every question "is this function convex?" ends up being answered in the negative---because the cases where …
Maximizing a convex function - Mathematics Stack Exchange
Solve a Convex optimization Problem which Involves Non Linear Constraints (Using $ \log \left( \cdot \right) $ Function) 0 Is minimizing the sum of the reciprocals equivalent to maximizing the …
optimization - Existence of minimizer for strongly convex function …
Jun 6, 2017 · I therefore provide here a very general Lemma (with valid reference): Every proper, lower-semi continuous, uniformly convex function on a Banach space is coercive and its …
real analysis - Midpoint-Convex and Continuous Implies Convex ...
Nov 18, 2011 · Below is the proof of the fact that every midpoint-convex function is rationally convex, which I copied from my older post on a different forum.
Definition of strongly convex - Mathematics Stack Exchange
It is easy to prove if you write out (2) based on the definition of convex function. Then what you need to know is that f(.) is convex and the norm is convex. Here any norm is ok, because of …
When is the difference of two convex functions convex?
Oct 5, 2014 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
How to determine whether a function of many variables is convex …
If the function is twice differentiable and the Hessian is positive semidefinite in the entire domain, then the function is convex. Note that the domain must be assumed to be convex too. If the …
real analysis - Subgradient of extension of convex function ...
Sep 24, 2017 · For a convex function, this domain must be a convex set. That said, we often adopt a so-called extended-real convention where we define the value of a convex function to …
analysis - Proving that a convex function is locally Lipschitz ...
Every convex function is continuous. 4. Can a function be neither convex nor concave everywhere? 4.