Tags » Convexity

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

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


Managers` total wealth analysis: should companies follow it in connection with stock price?

Is looking into the annual compensation enough to get an idea of how incentives are working? Shouldn`t companies look at stock related pay received in previous years, and assess if… 473 more words