Terminology for sets of minimum points
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In optimization there are definitions of concept like a local minimizer, strict local minimizer, isolated local minimizer, isolated critical point and so on. In my experience these always refer to a single point. I wonder if there is any established terminology for e.g. a path connected set of minimizers that are strict local minimizers when considered as a set?
Take for example a function $f:mathbb{R}^nrightarrowmathbb{R}$ and a path-connected set $S={xinmathbb{R}^n}$ of minimizers of $f$. Assume that there is a $delta>0$ such that $f|_{S}<f(y)$ for all $yin B_delta(S)={yinmathbb{R}^n,|,exists,xin S,,|y-x|<delta}$. Is there an established term for $S$? If so, could you provide a reference where it is used.
optimization terminology
asked Dec 23 '18 at 7:38
AsdfAsdf
422213
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In optimization there are definitions of concept like a local minimizer, strict local minimizer, isolated local minimizer, isolated critical point and so on. In my experience these always refer to a single point. I wonder if there is any established terminology for e.g. a path connected set of minimizers that are strict local minimizers when considered as a set?
Take for example a function $f:mathbb{R}^nrightarrowmathbb{R}$ and a path-connected set $S={xinmathbb{R}^n}$ of minimizers of $f$. Assume that there is a $delta>0$ such that $f|_{S}<f(y)$ for all $yin B_delta(S)={yinmathbb{R}^n,|,exists,xin S,,|y-x|<delta}$. Is there an established term for $S$? If so, could you provide a reference where it is used.
optimization terminology
asked Dec 23 '18 at 7:38
AsdfAsdf
422213
$endgroup$
add a comment |
$begingroup$
In optimization there are definitions of concept like a local minimizer, strict local minimizer, isolated local minimizer, isolated critical point and so on. In my experience these always refer to a single point. I wonder if there is any established terminology for e.g. a path connected set of minimizers that are strict local minimizers when considered as a set?
Take for example a function $f:mathbb{R}^nrightarrowmathbb{R}$ and a path-connected set $S={xinmathbb{R}^n}$ of minimizers of $f$. Assume that there is a $delta>0$ such that $f|_{S}<f(y)$ for all $yin B_delta(S)={yinmathbb{R}^n,|,exists,xin S,,|y-x|<delta}$. Is there an established term for $S$? If so, could you provide a reference where it is used.
optimization terminology
asked Dec 23 '18 at 7:38
AsdfAsdf
422213
$endgroup$
In optimization there are definitions of concept like a local minimizer, strict local minimizer, isolated local minimizer, isolated critical point and so on. In my experience these always refer to a single point. I wonder if there is any established terminology for e.g. a path connected set of minimizers that are strict local minimizers when considered as a set?
Take for example a function $f:mathbb{R}^nrightarrowmathbb{R}$ and a path-connected set $S={xinmathbb{R}^n}$ of minimizers of $f$. Assume that there is a $delta>0$ such that $f|_{S}<f(y)$ for all $yin B_delta(S)={yinmathbb{R}^n,|,exists,xin S,,|y-x|<delta}$. Is there an established term for $S$? If so, could you provide a reference where it is used.
optimization terminology
optimization terminology
asked Dec 23 '18 at 7:38
AsdfAsdf
422213
asked Dec 23 '18 at 7:38
AsdfAsdf
422213
asked Dec 23 '18 at 7:38
AsdfAsdf
422213
asked Dec 23 '18 at 7:38
AsdfAsdf
422213
asked Dec 23 '18 at 7:38
AsdfAsdf
422213
422213
add a comment |
add a comment |
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