Question

Minimize $\sum_{i=1}^n|x-a_i|$, $\max \{|x-a_i|, i=1,\cdots,n\}$, $\sum_{i=1}^n|x-a_i|^2$ and maximize $\Pi_{i=1}^n|x-a_i|$

score 1.1k · Answer 1 · 2018-08-16 21:34:57

1.1k

Views

Minimize $\sum_{i=1}^n|x-a_i|$, $\max \{|x-a_i|, i=1,\cdots,n\}$, $\sum_{i=1}^n|x-a_i|^2$ and maximize $\Pi_{i=1}^n|x-a_i|$

Published on 16 Aug 2018 - 21:34

score 389 · Answer 2 · 2018-08-16 22:04:43

389

Views

Minimizing the criterion function $f(a) = \int_0^1 [g(x) - p(x)]^2\ dx$ by a polynomial

Published on 16 Aug 2018 - 22:04

score 131 · Answer 3 · 2018-08-16 22:37:11

131

Views

$f^{(j)}(a) = 0$ except for the last derivative. Under which conditions $a$ can be a minimizer of $f$?

Published on 16 Aug 2018 - 22:37

score 44 · Answer 4 · 2026-03-26 12:37:46

44

Views

Proving maximum of $u$ on $\overline\Omega$ is achieved on $\partial \Omega$ using $Lv = \sum a_{jk}\partial_{jk} + \sum b_j(x)\partial_j$

Published on 26 Mar 2026 - 12:37

score 3.2k · Answer 5 · 2018-08-20 23:02:28

3.2k

Views

How to minimize $f(x) = \|Ax-b\|$

Published on 20 Aug 2018 - 23:02

score 267 · Answer 6 · 2018-08-21 08:13:36

267

Views

Monotonicity of function at a point

Published on 21 Aug 2018 - 8:13

score 302 · Answer 7 · 2018-08-22 21:34:47

302

Views

Show the optimal step to minimize $ax^tQx + b^tx + c$ has $\lambda = -\frac{d^t\nabla q(x)}{d^t\nabla^2q(x)d}$

Published on 22 Aug 2018 - 21:34

score 3.2k · Answer 8 · 2018-08-23 12:17:38

3.2k

Views

Every local minimum of $f(x) = \frac{1}{2}x^tAx + b^tx +c$ is also a global minimum

Published on 23 Aug 2018 - 12:17

score 104 · Answer 9 · 2018-08-25 17:08:50

104

Views

Find the maximum value of $A$

Published on 25 Aug 2018 - 17:08

score 169 · Answer 10 · 2018-08-25 20:10:57

169

Views

$f(\overline{x})=0$ but $\nabla^2 f(\overline{x})$ is not semidefinite positive. Prove there exists a descent direction

Published on 25 Aug 2018 - 20:10

score 247 · Answer 11 · 2018-08-27 02:36:37

247

Views

proving that $\arg\min f$ is also $\arg\min g\circ f$ for $g$ strictly increasing

Published on 27 Aug 2018 - 2:36

score 135 · Answer 12 · 2018-08-27 03:00:51

135

Views

$f(x) = (x_1-x_2^2)(x_1-\frac{1}{2}x_2^2)$, verify $\overline{x} = (0,0)^t$ is local min of $\phi(\lambda) = f(\overline{x}+\lambda d)$ but not of $f$

Published on 27 Aug 2018 - 3:00

score 306 · Answer 13 · 2018-08-27 03:30:16

306

Views

Finding $B$ that minimizes the frobenius norm $|A-B|_F$ for symmetric $B$

Published on 27 Aug 2018 - 3:30

score 109 · Answer 14 · 2018-08-27 23:21:54

109

Views

Find a descent direction $d^k$ orthogonal to direction $d^{k-1}$ which is linear comb. of $d^{k-1}$ and $\nabla f(x_k)$

Published on 27 Aug 2018 - 23:21

score 2.2k · Answer 15 · 2026-03-26 02:52:22

2.2k

Views

First Derivative Test on Parametric Equations

Published on 26 Mar 2026 - 2:52

List Question

Minimize $\sum_{i=1}^n|x-a_i|$, $\max \{|x-a_i|, i=1,\cdots,n\}$, $\sum_{i=1}^n|x-a_i|^2$ and maximize $\Pi_{i=1}^n|x-a_i|$

Minimizing the criterion function $f(a) = \int_0^1 [g(x) - p(x)]^2\ dx$ by a polynomial

$f^{(j)}(a) = 0$ except for the last derivative. Under which conditions $a$ can be a minimizer of $f$?

Proving maximum of $u$ on $\overline\Omega$ is achieved on $\partial \Omega$ using $Lv = \sum a_{jk}\partial_{jk} + \sum b_j(x)\partial_j$

How to minimize $f(x) = \|Ax-b\|$

Monotonicity of function at a point

Show the optimal step to minimize $ax^tQx + b^tx + c$ has $\lambda = -\frac{d^t\nabla q(x)}{d^t\nabla^2q(x)d}$

Every local minimum of $f(x) = \frac{1}{2}x^tAx + b^tx +c$ is also a global minimum

Find the maximum value of $A$

$f(\overline{x})=0$ but $\nabla^2 f(\overline{x})$ is not semidefinite positive. Prove there exists a descent direction

proving that $\arg\min f$ is also $\arg\min g\circ f$ for $g$ strictly increasing

$f(x) = (x_1-x_2^2)(x_1-\frac{1}{2}x_2^2)$, verify $\overline{x} = (0,0)^t$ is local min of $\phi(\lambda) = f(\overline{x}+\lambda d)$ but not of $f$

Finding $B$ that minimizes the frobenius norm $|A-B|_F$ for symmetric $B$

Find a descent direction $d^k$ orthogonal to direction $d^{k-1}$ which is linear comb. of $d^{k-1}$ and $\nabla f(x_k)$

First Derivative Test on Parametric Equations

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