Tags » Convexity

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


Strong Duality and Slater's Theorem

I left off a few days ago with my explanation of Weak Duality. Today, I will continue with the discussion of strong duality, which states… 1,092 more words


Lagrangian Dual Problem and Weak Duality

Lagrangian Dual Problem

I left off in my last post on the Lagrangian dual with the observation that we can turn the Lagrangian dual into the dual we are used to seeing as the dual LP, via a simple transformation. 680 more words