Tags » Convexity

Pretty convexity result

Where here we discover some interesting facts about continuous convex functions.

We know that a function is convex if

for all and .

We see that if is a continuous function, then an equivalent condition for convexity is that either of the following inequalities holds 108 more words

Variational Analysis

optimal simulation on a convex set

This morning, we had a jam session at the maths department of Paris-Dauphine where a few researchers & colleagues of mine presented their field of research to the whole department. 286 more words


extended formulation of the convex recoloring problem on a tree

use motivation ” convex recoloring problem ” phylogenetic tree protein- protein- interaction – net ( PPIN) 6 pages analysis compare two methods of population Hi:n1=n2 H1:n1>n2 branching point 1- extinct 2- hypothesized convexity is require for coloring two independunt subsets are not colore. 22 more words


Bounded convex function with no continuous boundary extension

Suppose is a convex function on a bounded convex domain . Does it have a continuous extension to ?

Of course not if is unbounded, like on the interval . 440 more words


Unconstrained minimization: Gradient descent algorithm

Theorem 1 Let be a convex and a -smooth function. Then, for any ,

Proof: Let . Then,

where follows by using gradient inequality for the term since is a convex function, and using the -smoothess of for the term, and follows by substituting . 557 more words

EE6151: Convex Optimization Algorithms