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 function is 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 convexity is present tend to be somewhat obvious. For general questions of computing derivatives involving vectors and matrices, the Matrix Cookbook is an essential resource.

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 sum of the non-reciprocals, when the variables are coupled?

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 subdifferential is onto. Lemma.

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 any norm is convex. Then the problem is proved.

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 developers to learn, share their knowledge, and build their careers.

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 Hessian has a negative eigenvalue at a point in the interior of the domain, then the function is …

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 be $+\infty$ outside of its domain; this enables us to talk about it as defined on all of $\mathbb{R}^n$.

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