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

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

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

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

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

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

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

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