Timeline for KKT in a nutshell graphically
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Sep 1, 2018 at 18:10 | history | suggested | frt132 | CC BY-SA 4.0 |
wrg, ts not interesx or not, just toolx, nonerx. otherx be any interex nmw
|
| Sep 1, 2018 at 9:15 | review | Suggested edits | |||
| S Sep 1, 2018 at 18:10 | |||||
| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
replaced http://stats.stackexchange.com/ with https://stats.stackexchange.com/
|
|
| Jan 25, 2017 at 7:53 | comment | added | Matthew Gunn | The basic KKT theorem says that if the KKT conditions aren't satisfied at a point $\mathbf{x}$, then the point $\mathbf{x}$ isn't optimal. The KKT conditions are necessary for an optimum but not sufficient. (For example, if the function has saddle points, local minima etc... the KKT conditions may be satisfied but the point isn't optimal!) For certain classes of problems (eg. convex problem where Slater's condition holds), the KKT conditions become sufficient conditions. | |
| Jan 18, 2017 at 3:38 | history | edited | mon | CC BY-SA 3.0 |
deleted 89 characters in body
|
| Jan 17, 2017 at 8:48 | history | edited | mon | CC BY-SA 3.0 |
added 588 characters in body
|
| Jan 17, 2017 at 0:05 | comment | added | Matthew Gunn | The basic idea of the complementary slackness condition (i.e. $\lambda g(\mathbf{x}) = 0$ where $g(\mathbf{x}) \leq 0$ is a constraint) is that if the constraint is slack (i.e.$g(\mathbf{x}) < 0$) at the optimal $\mathbf{x}$, then the penalty $\lambda$ for tightening the constraint is 0. And if there's a positive penalty $\lambda$ for tightening the constraint, then the constraint must be binding (i.e. $g(\mathbf{x}) = 0$). If traffic is flowing smoothly, the bridge toll $\lambda$ for another car is zero. And if the bridge toll $\lambda > 0$, then the bridge must be at the capacity limit. | |
| Jan 16, 2017 at 23:34 | history | edited | mon | CC BY-SA 3.0 |
added 6 characters in body
|
| Jan 14, 2017 at 0:11 | comment | added | Matthew Gunn | (1) If constraints don't bind, the optimization problem with the constraints has the same solution as the optimization problem without the constraints. (2) Neither $f$ need be convex nor $g$ need be linear for KKT conditions to be necessary at an optimum. (3) You do need special conditions (eg. convex problem where Slater condition holds) for KKT conditions holding to be sufficient conditions for an optimum. | |
| Jan 13, 2017 at 22:38 | answer | added | Matthew Gunn | timeline score: 8 | |
| Jan 13, 2017 at 17:38 | answer | added | Mark L. Stone | timeline score: 5 | |
| Jan 13, 2017 at 1:54 | comment | added | user23658 | This question may garner more attention on the mathematics site; KKT conditions are not necessarily "statistical". Statisticians borrow these and other results from numerical analysis to solve interesting statistical problems, but this is more of a mathematics question. | |
| Jan 13, 2017 at 0:59 | history | edited | mon | CC BY-SA 3.0 |
added 55 characters in body; edited title
|
| Jan 12, 2017 at 9:15 | history | edited | mon | CC BY-SA 3.0 |
added 122 characters in body
|
| Jan 11, 2017 at 23:39 | history | tweeted | twitter.com/StackStats/status/819327893604073472 | ||
| Jan 10, 2017 at 23:10 | history | edited | mon | CC BY-SA 3.0 |
added 9 characters in body
|
| Jan 10, 2017 at 21:05 | history | edited | mon | CC BY-SA 3.0 |
added 100 characters in body
|
| Jan 10, 2017 at 20:54 | history | edited | mon | CC BY-SA 3.0 |
added 9 characters in body
|
| Jan 10, 2017 at 5:48 | history | edited | mon | CC BY-SA 3.0 |
added 134 characters in body
|
| Jan 10, 2017 at 2:28 | history | edited | mon | CC BY-SA 3.0 |
deleted 4 characters in body
|
| Jan 10, 2017 at 2:27 | review | First posts | |||
| Jan 10, 2017 at 3:11 | |||||
| Jan 10, 2017 at 2:22 | history | asked | mon | CC BY-SA 3.0 |