Question

How to show directly $\min \frac{1}{2}\|x-z\|_2^2$ has a unique global minimizer over $Ax=b$?

score 939 · Answer 1 · 2026-04-13 19:52:33

939

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How to show directly $\min \frac{1}{2}\|x-z\|_2^2$ has a unique global minimizer over $Ax=b$?

Published on 13 Apr 2026 - 19:52

score 37 · Answer 2 · 2026-04-17 11:44:43

37

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Maximize $|\sum_{n=1}^N a_n|^2-\max\limits_{1\leq k\leq N}|\sum_{n=1}^N(-1)^{\delta_{k,n}}a_n|^2$ subject to $~\sum_{n=1}^N|a_n|^2=1$

Published on 17 Apr 2026 - 11:44

score 1k · Answer 3 · 2026-04-06 22:51:32

1k

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Extreme values of ${x^3 + y^3 + z^3 - 3xyz}$ subject to ${ax + by + cz =1}$ using Lagrange Multipliers

Published on 06 Apr 2026 - 22:51

score 91 · Answer 4 · 2026-04-12 03:41:29

91

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matlab - Optimization with inverse and pseudoinverse

Published on 12 Apr 2026 - 3:41

score 40 · Answer 5 · 2026-04-07 00:33:28

40

Views

Is there a way to qualify the difficulty of solving nonlinearprogramming?

Published on 07 Apr 2026 - 0:33

score 131 · Answer 6 · 2026-04-15 09:23:28

131

Views

Prove / Disprove that $E\big((X−a)^4\big)$ is minimized when $a=E(X)$.

Published on 15 Apr 2026 - 9:23

score 301 · Answer 7 · 2026-04-07 00:39:45

301

Views

orthogonal projection in projected gradient descent.

Published on 07 Apr 2026 - 0:39

score 306 · Answer 8 · 2026-04-13 12:22:23

306

Views

Ratio of maximum sums in table

Published on 13 Apr 2026 - 12:22

score 236 · Answer 9 · 2026-04-12 00:32:58

236

Views

How to show $x_* \in R(A^T) +z $ is the global minimizer of $\min \frac{1}{2}\|x-z\|_2^2$ over $Ax=b$?

Published on 12 Apr 2026 - 0:32

score 99 · Answer 10 · 2026-04-17 04:41:02

99

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Show that $C \subseteq D$ only if $\sigma_C(x) \leq \sigma_D(x)$ $\forall x \in \mathbb{R}^n$

Published on 17 Apr 2026 - 4:41

score 169 · Answer 11 · 2026-04-14 17:50:55

169

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Maximize $\det X$, subject to $X_{ii}\leq P_i$, where $X>0$

Published on 14 Apr 2026 - 17:50

score 252 · Answer 12 · 2026-03-26 07:37:29

252

Views

Does ADMM work for nonconvex optimization problems?

Published on 26 Mar 2026 - 7:37

score 238 · Answer 13 · 2026-04-15 23:27:02

238

Views

Find optimal number of videoclips to watch (depending on length) to get Maximum points.

Published on 15 Apr 2026 - 23:27

score 149 · Answer 14 · 2026-03-25 19:03:02

149

Views

Level sets of $C^1$ function on Riemannian manifold

Published on 25 Mar 2026 - 19:03

score 747 · Answer 15 · 2026-03-25 15:58:35

747

Views

Large Scale Quadratic Form with Linear Box Constraints

Published on 25 Mar 2026 - 15:58

List Question

How to show directly $\min \frac{1}{2}\|x-z\|_2^2$ has a unique global minimizer over $Ax=b$?

Maximize $|\sum_{n=1}^N a_n|^2-\max\limits_{1\leq k\leq N}|\sum_{n=1}^N(-1)^{\delta_{k,n}}a_n|^2$ subject to $~\sum_{n=1}^N|a_n|^2=1$

Extreme values of ${x^3 + y^3 + z^3 - 3xyz}$ subject to ${ax + by + cz =1}$ using Lagrange Multipliers

matlab - Optimization with inverse and pseudoinverse

Is there a way to qualify the difficulty of solving nonlinearprogramming?

Prove / Disprove that $E\big((X−a)^4\big)$ is minimized when $a=E(X)$.

orthogonal projection in projected gradient descent.

Ratio of maximum sums in table

How to show $x_* \in R(A^T) +z $ is the global minimizer of $\min \frac{1}{2}\|x-z\|_2^2$ over $Ax=b$?

Show that $C \subseteq D$ only if $\sigma_C(x) \leq \sigma_D(x)$ $\forall x \in \mathbb{R}^n$

Maximize $\det X$, subject to $X_{ii}\leq P_i$, where $X>0$

Does ADMM work for nonconvex optimization problems?

Find optimal number of videoclips to watch (depending on length) to get Maximum points.

Level sets of $C^1$ function on Riemannian manifold

Large Scale Quadratic Form with Linear Box Constraints

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