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 …

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 …

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 …

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 …

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.

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 …

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 …

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 …

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 …

Every convex function is continuous. 4. Can a function be neither convex nor concave everywhere? 4.