Bad convex functions
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Why are functions of the form $ f_{m} (x) = eta_{p+1}(A_m x) - x_1$ bad, where $eta_{p+1} = frac{1}{p+1}sum_{i=1}^{n}(x_i)^{p+1}$, $A_m = begin{pmatrix}U_m & 0 \ 0 &I_{n-m} end{pmatrix}$, $U_m = begin{pmatrix} 1 & -1 & 0& ... \
0&1&-1&0&....\
&&...&&\
0&...&0&1 end{pmatrix} in mathbb{R}^{mtimes m}$.
In https://arxiv.org/pdf/1705.07260.pdf and https://alfresco.uclouvain.be/alfresco/service/guest/streamDownload/workspace/SpacesStore/aabc2323-0bc1-40d4-9653-1c29971e7bd8/coredp2018_05web.pdf?guest=true this family of functions are used for estimate lower bound complexity.
I don't really understand explanation from first article. Could someone explain more clearly?
optimization convex-optimization numerical-optimization
asked Nov 1 at 22:16
Albert Nagapetyan
84
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Why are functions of the form $ f_{m} (x) = eta_{p+1}(A_m x) - x_1$ bad, where $eta_{p+1} = frac{1}{p+1}sum_{i=1}^{n}(x_i)^{p+1}$, $A_m = begin{pmatrix}U_m & 0 \ 0 &I_{n-m} end{pmatrix}$, $U_m = begin{pmatrix} 1 & -1 & 0& ... \
0&1&-1&0&....\
&&...&&\
0&...&0&1 end{pmatrix} in mathbb{R}^{mtimes m}$.
In https://arxiv.org/pdf/1705.07260.pdf and https://alfresco.uclouvain.be/alfresco/service/guest/streamDownload/workspace/SpacesStore/aabc2323-0bc1-40d4-9653-1c29971e7bd8/coredp2018_05web.pdf?guest=true this family of functions are used for estimate lower bound complexity.
I don't really understand explanation from first article. Could someone explain more clearly?
optimization convex-optimization numerical-optimization
asked Nov 1 at 22:16
Albert Nagapetyan
84
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Why are functions of the form $ f_{m} (x) = eta_{p+1}(A_m x) - x_1$ bad, where $eta_{p+1} = frac{1}{p+1}sum_{i=1}^{n}(x_i)^{p+1}$, $A_m = begin{pmatrix}U_m & 0 \ 0 &I_{n-m} end{pmatrix}$, $U_m = begin{pmatrix} 1 & -1 & 0& ... \
0&1&-1&0&....\
&&...&&\
0&...&0&1 end{pmatrix} in mathbb{R}^{mtimes m}$.
In https://arxiv.org/pdf/1705.07260.pdf and https://alfresco.uclouvain.be/alfresco/service/guest/streamDownload/workspace/SpacesStore/aabc2323-0bc1-40d4-9653-1c29971e7bd8/coredp2018_05web.pdf?guest=true this family of functions are used for estimate lower bound complexity.
I don't really understand explanation from first article. Could someone explain more clearly?
optimization convex-optimization numerical-optimization
asked Nov 1 at 22:16
Albert Nagapetyan
84
Why are functions of the form $ f_{m} (x) = eta_{p+1}(A_m x) - x_1$ bad, where $eta_{p+1} = frac{1}{p+1}sum_{i=1}^{n}(x_i)^{p+1}$, $A_m = begin{pmatrix}U_m & 0 \ 0 &I_{n-m} end{pmatrix}$, $U_m = begin{pmatrix} 1 & -1 & 0& ... \
0&1&-1&0&....\
&&...&&\
0&...&0&1 end{pmatrix} in mathbb{R}^{mtimes m}$.
In https://arxiv.org/pdf/1705.07260.pdf and https://alfresco.uclouvain.be/alfresco/service/guest/streamDownload/workspace/SpacesStore/aabc2323-0bc1-40d4-9653-1c29971e7bd8/coredp2018_05web.pdf?guest=true this family of functions are used for estimate lower bound complexity.
I don't really understand explanation from first article. Could someone explain more clearly?
optimization convex-optimization numerical-optimization
optimization convex-optimization numerical-optimization
asked Nov 1 at 22:16
Albert Nagapetyan
84
asked Nov 1 at 22:16
Albert Nagapetyan
84
edited Nov 16 at 16:33
asked Nov 1 at 22:16
Albert Nagapetyan
84
asked Nov 1 at 22:16
Albert Nagapetyan
84
asked Nov 1 at 22:16
Albert Nagapetyan
84
84
add a comment |
add a comment |
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