Timeline for Linear function on a non convex domain
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 31, 2016 at 21:08 | comment | added | VictorZurkowski | (where ccc = "closed convex hull") | |
| Aug 31, 2016 at 21:07 | comment | added | VictorZurkowski | Right. The least concave majorant should involve only the points that matter. Take $g_i^*(u) = \inf\{h(u)| h \text{ is defined on } ccc(D_{i-1}), h \text{ is concave on $ccc(D_{i-1})$, } g_i(\zeta) \le h(\zeta) \text{ for all }\zeta \in ccc(D_{i-1}\}$ | |
| Aug 31, 2016 at 20:48 | history | edited | VictorZurkowski | CC BY-SA 3.0 |
added 2 characters in body
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| Aug 31, 2016 at 8:26 | comment | added | mono | Thank you for the answer, the first part is very clear, but I am not convinced that what you claim in the second part of your answer is true: suppose for example that it holds for a particular $f, g: [-1, 1] \rightarrow [-1, 1]$. Then, adding a new linear piece to the functions such that $f(2) = -M$ and $g(2)=M$ for a big $M$ would make the convex hull of the $D_i$'s very large by adding a set of points which will never be feasible for the solution, since $x_i \in [-1, 1]$ by our assumption on $f$ and $g$. | |
| Aug 30, 2016 at 5:14 | history | answered | VictorZurkowski | CC BY-SA 3.0 |