1
vote
1answer
58 views

Please explain this theorem with picture

I logically understand this theorem, but I don't intuitively understand with picture. Let $S$ be a nonempty convex open set in $\mathbb R^n$ and let $f\colon S\to\mathbb R$ be differentiable on ...
7
votes
1answer
188 views

How to understand convex duality intuitively

Is there an intuitive way to understand the convex duality? If the primal problem is minimization, the dual is maximization over another set of variables - but I would love to have a geometric ...
0
votes
2answers
342 views

Intuition behind gradient VS curvature

In Newton's method, one computes the gradient of a cost function, (the 'slope') as well as its hessian matrix, (ie, second derivative of the cost function, or 'curvature'). I understand the intuition, ...
4
votes
4answers
532 views

Summary of Optimization Methods.

Context: So in a lot of my self-studies, I come across ways to solve problems that involve optimization of some objective function. (I am coming from signal processing background). Anyway, I seem to ...
10
votes
5answers
778 views

Why is convexity more important than quasi-convexity in optimization?

In the mathematical optimization literature it is common to distinguish problems according to whether or not they are convex. The reason seems to be that convex problems are guaranteed to have ...