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Results tagged with convexity
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user 13385
For questions involving the concept of convexity
1
vote
2
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1k
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Convex polynomial homogenization and convexity
The function whose convexity I would like to show in the variables $(a,p_1,\dots,p_N)$ for $a > 0$ and under some bound on the magnitudes of the $p_n$'s (I suspect the bound will be $\vert p_n \vert < …
- 73
1
vote
Accepted
Convex polynomial homogenization and convexity
Convexity of the function $a_0 \sqrt{\prod_{j=1}^{N_t} \left( 1 + \vert p_j \vert^2 / a_0^2 \right)}$ for $a_0 > 0$ and $\vert p_j \vert \leq a_0$ follows from the fact that the perspective of a convex …
- 73
4
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1
answer
411
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Convexity of $\frac{1}{2}\vert x_1 + x_2 + x_3 - x_1x_2x_3\vert^2$
Anybody have any tips on how to show that the function $\frac{1}{2}\vert x_1 + x_2 + x_3 - x_1x_2x_3\vert^2$ is convex in $\mathbf{x}$, where $\vert x_i \vert \leq 1$?
This comes from the following …
- 73
1
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0
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236
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Convexity of a constrained optimization problem
Hi, this is a continuation of a previous question I asked about the convexity of an optimization problem I am working with. …
- 73