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align chapter12 contents #136

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May 22, 2021
Merged

align chapter12 contents #136

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2043ad5
rename for consistency
hunhoon21 May 22, 2021
3b0cbc3
fix url
hunhoon21 May 22, 2021
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fix url
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hunhoon21 committed May 22, 2021
commit 3b0cbc38f97da25a0e0b5aa4159831023e79aa82
2 changes: 1 addition & 1 deletion chapter16/_posts/21-03-31-16_02_optimality_conditions.md
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Expand Up @@ -29,7 +29,7 @@ MathJax.Hub.Config({

주어진 primal problem이 convex일때, KKT conditions는 primal & dual optimal에 대한 충분조건이 된다. 즉, $$f, h_1, \dots, h_m$$가 convex이고 $$l_1, \dots, l_r$$가 affine일때, $$x^\star, u^\star, v^\star$$가 다음의 KKT conditions를 만족한다면 $$x^\star$$와 $$(u^\star, v^\star)$$는 zero duality gap인 primal & dual optimal이다. ($$f, h_1, \dots, h_m, l_1, \dots, l_r$$는 미분 가능하다고 가정한다.) <br>

* 참고: [12-01 KKT conditions]({% post_url chapter12/21-04-02-12_KKT_conditions %})
* 참고: [12-01 KKT conditions]({% post_url chapter12/21-04-02-12_00_KKT_conditions %})

#### KKT conditions for the given primal problem
>$$
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2 changes: 1 addition & 1 deletion chapter17/_posts/21-05-01-17_01_barrier_method_duality_optimality_revisited.md
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Expand Up @@ -85,7 +85,7 @@ $$f,h_1,...h_m$$은 convex 이고 미분 가능하고, 또한 주어진 문제

여기서 $$U$$는 $$\text{diag}(u)$$를 뜻하며, $$∇h(x)$$는 $$ [ ∇h_1(x) ··· ∇h_m(x) ]$$를 의미한다.

* 자세한 내용은 [12장 KKT conditions]({% post_url chapter12/21-04-02-12_KKT_conditions %}) 참조
* 자세한 내용은 [12장 KKT conditions]({% post_url chapter12/21-04-02-12_00_KKT_conditions %}) 참조

## Central path equations
함수 $$f(x)$$를 barrier 문제로 아래와 같이 재정의 할 수 있다.<br>
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