Question

minima of a multivariate function

score 121 · Answer 1 · 2026-04-09 18:38:52

121

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minima of a multivariate function

Published on 09 Apr 2026 - 18:38

score 337 · Answer 2 · 2026-04-13 17:08:39

337

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Primal-dual correspondence in the simplex method

Published on 13 Apr 2026 - 17:08

score 180 · Answer 3 · 2026-04-12 08:31:13

180

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Does nonstandard analysis allow for a more powerful second derivative test?

Published on 12 Apr 2026 - 8:31

score 51 · Answer 4 · 2026-03-26 00:58:24

51

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Ensuring global minima minimizing a polynomial/smooth function numerically

Published on 26 Mar 2026 - 0:58

score 71 · Answer 5 · 2026-04-12 07:47:35

71

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A difference equation problem $z_j = z_{j-1} (1 - (1-a)x_j)$

Published on 12 Apr 2026 - 7:47

score 2.7k · Answer 6 · 2026-04-16 17:20:49

2.7k

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$f$ convex $\iff$ $f(y) \ge f(x) + \nabla^Tf(x)(y-x)$ and $f$ is convex $\iff$ $\nabla^2f(x)\ge 0$

Published on 16 Apr 2026 - 17:20

score 54 · Answer 7 · 2026-04-11 17:48:10

54

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Find the quickest path through a mixed-density fluid

Published on 11 Apr 2026 - 17:48

score 202 · Answer 8 · 2026-04-16 07:04:35

202

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Prove $f(y) = \min \{|y-x|, x\in S\}$ is convex when $S = \{x\in\mathbb{R}^2|ax_1 + bx_2 = c\}$

Published on 16 Apr 2026 - 7:04

score 620 · Answer 9 · 2026-04-09 07:32:18

620

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Exercise 1.21 of Villani Topics in Optimal Transportation

Published on 09 Apr 2026 - 7:32

score 5.1k · Answer 10 · 2026-04-13 01:35:01

5.1k

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Why do we need sub-gradient methods for non-differentiable functions?

Published on 13 Apr 2026 - 1:35

score 175 · Answer 11 · 2026-04-15 17:51:26

Solve $\min_{\mathbf{x},\mathbf{R}}\left\|\mathbf{y}-\mathbf{x}\right\|_{\mathbf{R}}^2$ s.t. $\mathbf{A}\mathbf{x}=\mathbf{0}$; $\mathbf{R}\succeq0$

score 1.1k · Answer 12 · 2026-04-15 12:55:49

1.1k

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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 15 Apr 2026 - 12:55

score 31 · Answer 13 · 2026-04-14 05:42:21

31

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Given k food items, with constraints being the total weights of various nutrients, how do I find the minimum price p?

Published on 14 Apr 2026 - 5:42

score 392 · Answer 14 · 2026-04-16 00:07:39

392

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

Published on 16 Apr 2026 - 0:07

score 134 · Answer 15 · 2026-04-14 15:18:34

134

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

Published on 14 Apr 2026 - 15:18

List Question

minima of a multivariate function

Primal-dual correspondence in the simplex method

Does nonstandard analysis allow for a more powerful second derivative test?

Ensuring global minima minimizing a polynomial/smooth function numerically

A difference equation problem $z_j = z_{j-1} (1 - (1-a)x_j)$

$f$ convex $\iff$ $f(y) \ge f(x) + \nabla^Tf(x)(y-x)$ and $f$ is convex $\iff$ $\nabla^2f(x)\ge 0$

Find the quickest path through a mixed-density fluid

Prove $f(y) = \min \{|y-x|, x\in S\}$ is convex when $S = \{x\in\mathbb{R}^2|ax_1 + bx_2 = c\}$

Exercise 1.21 of Villani Topics in Optimal Transportation

Why do we need sub-gradient methods for non-differentiable functions?

Solve $\min_{\mathbf{x},\mathbf{R}}\left\|\mathbf{y}-\mathbf{x}\right\|_{\mathbf{R}}^2$ s.t. $\mathbf{A}\mathbf{x}=\mathbf{0}$; $\mathbf{R}\succeq0$

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 $\Pi_{i=1}^n|x-a_i|$

Given k food items, with constraints being the total weights of various nutrients, how do I find the minimum price p?

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 $f$?

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