Timeline for Uniqueness of a Solution for a Convex Optimization Problem
Current License: CC BY-SA 3.0
33 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 29, 2020 at 9:45 | vote | accept | Seyhmus Güngören | ||
| Dec 11, 2017 at 20:45 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 11, 2017 at 20:40 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Oct 12, 2017 at 19:40 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Sep 12, 2017 at 18:44 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 13, 2017 at 18:41 | answer | added | Seyhmus Güngören | timeline score: 1 | |
| Aug 10, 2017 at 1:16 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 238 characters in body
|
| S Aug 1, 2017 at 21:49 | history | bounty ended | CommunityBot | ||
| S Aug 1, 2017 at 21:49 | history | notice removed | CommunityBot | ||
| Jul 27, 2017 at 23:27 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 1 character in body
|
| Jul 27, 2017 at 3:47 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
deleted 28 characters in body
|
| Jul 25, 2017 at 13:43 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 413 characters in body
|
| Jul 24, 2017 at 21:18 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
deleted 14 characters in body
|
| Jul 24, 2017 at 21:13 | comment | added | Seyhmus Güngören | @MattF. alright, let me edit then. | |
| Jul 24, 2017 at 21:01 | comment | added | user44143 | This would be easier to read with $f_l, q_0, f_u, g_l, q_1, g_u$ replaced by $f_L, f, f_U, g_L, g, g_U$. | |
| S Jul 24, 2017 at 20:43 | history | bounty started | Seyhmus Güngören | ||
| S Jul 24, 2017 at 20:43 | history | notice added | Seyhmus Güngören | Draw attention | |
| Jul 21, 2017 at 20:29 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 145 characters in body
|
| Jul 14, 2017 at 15:58 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 1 character in body
|
| Jul 12, 2017 at 15:18 | history | edited | Seyhmus Güngören |
edited tags
|
|
| Jul 10, 2017 at 18:45 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 26 characters in body
|
| Jul 9, 2017 at 20:06 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 1 character in body
|
| Jul 8, 2017 at 19:15 | comment | added | Seyhmus Güngören | There is no meaning of the question if one gets a result $q_0=q_1$. One chooses normally the functions $f_l$, $g_l$, $f_u$ and $g_u$ such that $q_0$ is distinct from $q_1$. Namely $f_u=g_u$ and $f_l=g_l$ are not allowed. Basilcally, this case is out of consideration. | |
| Jul 8, 2017 at 18:58 | comment | added | Paata Ivanishvili | In this case the maximizer $(q_{1}, q_{0})$ does not exist when $0\leq f_{\ell} = g_{\ell} < f_{u}=g_{u}$ a.e.. So the question about uniqueness does not make sense. | |
| Jul 8, 2017 at 18:26 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 9 characters in body
|
| Jul 8, 2017 at 18:25 | comment | added | Seyhmus Güngören | @PaataIvanisvili $q_0$ and $q_1$ are distinct. Sorry I forgot it in the question. Editing now. | |
| Jul 8, 2017 at 18:16 | comment | added | Paata Ivanishvili | For each fixed $u \in (0,1)$ there can be infinitely many solutions depending on $f_{u}, g_{u}, f_{\ell}, g_{\ell}$. Consider the scenario when $0\leq f_{\ell}=g_{\ell}<f_{u}=g_{u}$ a.e.. In this case the extremizers are $q_{0}=q_{1}=h$ where $h$ is any integrable function with $f_{\ell} \leq h \leq f_{u}$ and $\int_{\Omega}h d\mu=1$. Indeed, by Holder's inequality we always have $$ \int_{\Omega} q_{1}^{u}q_{0}^{1-u} d\mu \leq \left( \int_{\Omega} q_{1}\right)^{u}\left(\int_{\Omega} q_{0} d\mu \right)^{1-u}=1 $$ and equality is attained if and only if $q_{1}(x) = \lambda\, q_{0}(x)$. | |
| Jul 8, 2017 at 14:53 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 109 characters in body
|
| Jul 8, 2017 at 14:49 | comment | added | Seyhmus Güngören | @YoavKallus exactly!! I will add this information to the question. Thx for reminding. | |
| Jul 8, 2017 at 14:24 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 83 characters in body
|
| Jul 8, 2017 at 14:09 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 25 characters in body
|
| Jul 8, 2017 at 13:31 | history | edited | Seyhmus Güngören | CC BY-SA 3.0 |
added 4 characters in body
|
| Jul 7, 2017 at 21:53 | history | asked | Seyhmus Güngören | CC BY-SA 3.0 |