- #1

perplexabot

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## Homework Statement

Show if the set is convex or not!

S2 =

## Homework Equations

I know that to show a set is convex you can either use the definition or show that the set can be obtained from known convex sets under operations that preserve convexity.

Convex definition: x1*Theta + (1 - Theta)*x2 ∈ S2

Ops that preserve convex sets (that i know of): Intersection, affine functions, perspective functions, linear functionals.

This formula may come in handy:

## The Attempt at a Solution

I was able to rewrite the set as:

I have no idea if that will help me and I also have no idea where to go from here!!! Using the definition I end up with sums in the log function which leads me no where. I have a feeling this set is not convex but once again I am not sure.

Please any help will be greatly appreciated as I have been thinking about it for a while.

Thank you.

PS: I am able to prove simple things like the convexity of a norm ball or polyhedra but I am not able to do this one.

EDIT: I have scanned a better attempt at this problem, however I am still not able to do it. I feel defeated, it feels bad : (

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