Timeline for Generalization of standard convex problem
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 1, 2015 at 15:20 | comment | added | gerw | I do not have any specific suggestions. Farkas' lemma should be contained in any (introductory) book on non-linear optimization. Otherwise, consult any (introductory) book on convex optimization. | |
| Nov 1, 2015 at 5:56 | comment | added | behrad mahboobi | can you take a look on my new question please. mathoverflow.net/questions/222346/… | |
| Nov 1, 2015 at 3:42 | vote | accept | behrad mahboobi | ||
| Nov 1, 2015 at 3:39 | comment | added | behrad mahboobi | thank you so much Gerw, do u proposed any text book in this field that cover tangent cone, fakas lemma and related topics in convex analysis? | |
| Oct 31, 2015 at 19:49 | comment | added | gerw | No. $S$ is always convex by assumption. You only drop the non-active constraints in the proof, exactly at those points, where the derivatives $g_i'(x)$ appear. | |
| Oct 31, 2015 at 19:33 | comment | added | behrad mahboobi | then we reduce to a nonconvex set to obtain a tangent cone which tangent cone is only defined for convex sets! | |
| Oct 31, 2015 at 19:09 | comment | added | gerw | Then, you write down the same proof, but leave out the non-active constraints. This is typically done by introducing the set $A(x) = \{i : g_i(x) = 0\}$ of active constraints. | |
| Oct 31, 2015 at 19:07 | comment | added | behrad mahboobi | what if both constraints aren't active in the same time ? can we claim that in any conditoon KKT condition result in $$-\nabla f (x) \in \{d : g_1'(x) \, d \le 0, g_2'(x) \, d \le 0\}^\circ.$$, independent of the convesity of $f,S$? | |
| Oct 31, 2015 at 19:05 | vote | accept | behrad mahboobi | ||
| Oct 31, 2015 at 19:06 | |||||
| Oct 29, 2015 at 19:00 | history | answered | gerw | CC BY-SA 3.0 |