Tags » Convexity

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

CFA 1, Reading 58: Introduction to Measurement of Interest Rate Risk

This video covers the whole of Reading 58 of the CFA Level 1 curriculum. We examine price/yield behavior along the yield spectrum, and identify peculiarities and characteristics of bond prices as yield changes.  100 more words

Fixed Income

From Oberwolfach: The Topological Tverberg Conjecture is False

The topological Tverberg conjecture (discussed in this post), a holy grail of topological combinatorics, was refuted! The three-page paper “Counterexamples to the topological Tverberg conjecture” 254 more words


Constraint qualifications and subgradient sum rules

I am not an optimizer by training. My road to optimization went through convex analysis. I started with variational methods for inverse problems and mathematical imaging with the goal to derive properties of minimizers of convex functions. 630 more words