Questions tagged [cone]

For questions relating to the mathematical or geometric structure known as a cone.

Filter by
Sorted by
Tagged with
17
votes
3answers
231 views

How to take the dual of a conic optimization problem?

Given a conic problem $$\min \{c^\top x \mid Ax \succeq_\mathit{C} b\}$$ for an arbitrary cone $C$, how can I construct the dual to the problem? Moreover, in Linear Programming one constructs the ...
10
votes
1answer
148 views

Intuition behind SOCP and why it sometimes can be solved more efficiently than without transforming it into a SOCP?

I was doing an assignment regarding turbine placements, where one has to write and solve a maximisation problem. As I was reading into the topic, I came across the fact that I could transform the ...
8
votes
2answers
146 views

Convex Optimization: Separation of Cones

I am trying to solve Exercise 2.39 at Boyd and Vandenberghe's Convex Optimization book. In one source, the answer is given as: 2.39 Separation of cones. Let $K$ and $\tilde K$ be two convex cones ...
4
votes
1answer
246 views

Transforming a Quadratic constraint to SOCP

I have a problem similar to Markowitz portfolio optimization that I would like to transform into second-order cone programming. I have a linear objective function with a quadratic constraint (assuming ...
-2
votes
0answers
44 views

Separating hyperplanes [closed]

Let $C$ be finitely generated cone and let $x \notin C$. How can we show that there can only be finitely many separating hyperplanes between $C$ and $x$?
-2
votes
0answers
36 views

Help on understanding the proof [closed]

Could someone please explain the red parts which were not clear for me? (From page 6 of: http://www.personal.psu.edu/vvs3/IE597/ie597_lect4.pdf)