Question

Convex function inequalities with gradient being Lipschitz continuous, starting from $f(y)\le f(x)+(\nabla f(x))^T(y-x)+\frac{L}{2}\Vert y-x\Vert_2^2$

score 519 · Answer 1 · 2022-05-01 09:39:32

519

Views

Convex function inequalities with gradient being Lipschitz continuous, starting from $f(y)\le f(x)+(\nabla f(x))^T(y-x)+\frac{L}{2}\Vert y-x\Vert_2^2$

Published on 01 May 2022 - 9:39

score 41 · Answer 2 · 2026-03-31 20:54:50

41

Views

Solution of IVP is defined for all $t\in\mathbb{R}$ if $f$ is Lipschitz

Published on 31 Mar 2026 - 20:54

score 154 · Answer 3 · 2022-05-02 09:00:36

154

Views

Approximate a lower semi-continuous and bounded from below function by an increasing sequence $(f_n)$ of $n$-Lipschitz continuous functions

Published on 02 May 2022 - 9:00

score 32 · Answer 4 · 2022-05-02 18:38:12

32

Views

Checking out 2 proofs refered to Lipschitz-continuity

Published on 02 May 2022 - 18:38

score 290 · Answer 5 · 2022-05-03 18:08:21

290

Views

Showing that the best approximating linear map for a Lipschitz function is also Lipschitz

Published on 03 May 2022 - 18:08

score 68 · Answer 6 · 2022-05-03 18:38:18

Do the following functions $ f: \mathbb{R}^{2} \rightarrow \mathbb{R} $ satisfy a local or global Lipschitz condition with respect to $ x $?

score 65 · Answer 7 · 2022-05-05 09:55:09

65

Views

Check whether there is a global existence of solution of function $y'(x) = \frac{-y(x)}{1+e^{y(x)}}$?

Published on 05 May 2022 - 9:55

score 108 · Answer 8 · 2022-05-07 01:23:58

108

Views

Why is the function $\|\mathbf{J}\|_{\infty}$ $1$-Lipschitz w.r.t to the Euclidean norm?

Published on 07 May 2022 - 1:23

score 156 · Answer 9 · 2022-05-07 17:05:59

156

Views

Is $e^{-\int_0^t f(u)du} $ a Lipschitz function?

Published on 07 May 2022 - 17:05

score 170 · Answer 10 · 2022-05-10 20:09:11

170

Views

Definiteness of Nemytskii operator on space of continuous functions

Published on 10 May 2022 - 20:09

score 77 · Answer 11 · 2026-03-30 06:44:18

77

Views

Smoothness of the function $\lambda \mapsto \inf_{x \in \mathcal{C}}\|\lambda x - y\|^2$

Published on 30 Mar 2026 - 6:44

score 104 · Answer 12 · 2026-03-27 07:12:03

104

Views

Simple yet hard inequality with Lipschitz functions

Published on 27 Mar 2026 - 7:12

score 67 · Answer 13 · 2022-05-11 16:33:09

67

Views

Uniformly continuous function implies almost Lipschitz continous.

Published on 11 May 2022 - 16:33

score 549 · Answer 14 · 2022-05-11 20:20:52

549

Views

The space of Lipschitz continuous functions is dense in that of uniformly continuous functions?

Published on 11 May 2022 - 20:20

score 426 · Answer 15 · 2022-05-18 16:59:15

426

Views

One sided Lipschitz condition

Published on 18 May 2022 - 16:59

List Question

Convex function inequalities with gradient being Lipschitz continuous, starting from $f(y)\le f(x)+(\nabla f(x))^T(y-x)+\frac{L}{2}\Vert y-x\Vert_2^2$

Solution of IVP is defined for all $t\in\mathbb{R}$ if $f$ is Lipschitz

Approximate a lower semi-continuous and bounded from below function by an increasing sequence $(f_n)$ of $n$-Lipschitz continuous functions

Checking out 2 proofs refered to Lipschitz-continuity

Showing that the best approximating linear map for a Lipschitz function is also Lipschitz

Do the following functions $ f: \mathbb{R}^{2} \rightarrow \mathbb{R} $ satisfy a local or global Lipschitz condition with respect to $ x $?

Check whether there is a global existence of solution of function $y'(x) = \frac{-y(x)}{1+e^{y(x)}}$?

Why is the function $\|\mathbf{J}\|_{\infty}$ $1$-Lipschitz w.r.t to the Euclidean norm?

Is $e^{-\int_0^t f(u)du} $ a Lipschitz function?

Definiteness of Nemytskii operator on space of continuous functions

Smoothness of the function $\lambda \mapsto \inf_{x \in \mathcal{C}}\|\lambda x - y\|^2$

Simple yet hard inequality with Lipschitz functions

Uniformly continuous function implies almost Lipschitz continous.

The space of Lipschitz continuous functions is dense in that of uniformly continuous functions?

One sided Lipschitz condition

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