Questions tagged [cone]

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

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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
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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)
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 ...
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 ...
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 ...
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 ...