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5:27 AM
A new tag was created and added to 12 questions.
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Q: Differential characterization of monotone operators

Dat Ba TranGiven $D\subset \mathbb{R}^n$. $f:D\longrightarrow\mathbb{R}^n$ is said to be a monotone operator if $$\left\langle f(x)-f(y),x-y\right\rangle\ge 0,\text{ for all }x,y\in D.$$ I wonder if this hypothesis is true about monotone operators. Given $D\subset \mathbb{R}^n$ and a differentiable operat...

2
Q: Characterization of maximal monotone operators

PaoloI found the following theorem: Given $H$ Hilbert space and a monotone operator $A\colon H\rightarrow H$, then A is maximal monotone if and only if $\operatorname{Range}(A+I)=H$. Note that: $A$ monotone (multivalued) means that $\forall u,v \in H$ and $\forall f\in Au, g \in Av$, then $(u-v,f-g)...

0
Q: Monotone operator on $L^2(0,\infty)$

D GI trying to prove the following assestment Every linear monotone operator on $L^2 (0, \infty)$ is bounded Any ideas? Thank you

2
Q: Maximal monotone operator without convex domain?

dmw64I'm looking for an example of a (multi-valued) maximal monotone operator $A$ mapping a Banach space $X$ into its dual $X^*$ such that the domain $D(A)=\{x\in X: Ax\neq\emptyset\}$ is not convex. Preferably, the example should be simple (maybe with $X=\mathbb{R}^2$). Thanks a lot in advance for s...

2
Q: Resolvent of maximal-monotone operator

user202542I'm reading Barbus & Precupanu's 'Convexity and optimization in Banach spaces'. The authors define what I think is the resolvent for an operator $A: X \to X^*$ (or subset $A \subset X \times X^*$) where $X^*$ is the dual space: Let $ X,X^*$ be reflexive and strictly convex and $A$ maximal mon...

3
Q: Pseudo Monotone Operator

TomásSuppose $X$ is a real Reflexive Banach space. Let $A:X\rightarrow X^{\star}$ be a Pseudo Monotone operator, i.e. if $u_{n}\rightharpoonup u$ and $\limsup\langle Au_{n},u_{n}-u\rangle\leq 0$, then $$\langle Au,u-w\rangle\leq\liminf\langle Au_{n},u_{n}-w\rangle,\ \forall\ w\in X$$ where $\righthar...

1
Q: The meaning of a symbol in Monotone operator

asd123wwwI'm learning monotone operator these days and can't figure out the meaning of the symbol. If you know the symbol please tell me. Thanks for your time!

1
Q: Monotone condition for multivariable functions and monotone operators

ofir_13I am looking for a general definition of monotone condition for a function $G: \mathbb{R}^m \to \mathbb{R}^m$, and since I did not find a unique definition of monotone condition for multivariable function (see Monotonicity of function of two variables), I was wondering if the definition of monoto...

2
Q: Iterative Refinement and Monotone Operators

jjjjjjIn the paper Ernest K. Yyu, Stephen Noyd - A Primer on Monotone Operator Methods - Survey, the authors frame Iterative Refinement (of an approximate solution to a linear system $Ax=b$) in the context of monotone operators, Resolvents, and Cayley operators. They require $A+A^T \succeq 0$ to ensure...

1
Q: A question on maximal monotone operators

jafar Definition: Let $H$ a Hilbert space. An unbounded linear operator $A: D(A) \subseteq H \to H$ is said to be monotone if it satisfies $$\forall v \in D(A),\ (Av, v) \ge 0 $$ It is called maximal monotone if, in addition, $R(I + A) = H$, i.e., $\forall f \in H,\ \exists u \in D(A) \tex...

3
Q: Is the composition of monotone operators monotone?

user693Let $H$ be a real Hilbert space with inner product $\langle\cdot, \cdot \rangle: H \times H \rightarrow \mathbb{R}$, and induced norm $\left\| \cdot \right\|: H \rightarrow \mathbb{R}_{\geq 0}$. Let $A, B : H \rightarrow H$ be monotone operators, that is (for both $A$ and $B$) $$ \langle A x - ...

2
Q: Is this operator monotone?

miningConsider a convex optimization problem. $$\min_{u\in\Re^k} f(u)$$ s.t. $g_i(u)\leq0,\ i=1,\ldots,m$ Let $F(x)=F(u,\lambda)=(f'(u)+\sum_{i=1}^m\lambda_ig_i'(u),-g_1(u),\ldots,-g_m(u)):\Re^n\rightarrow\Re^n$, ($n=k+m$) $G=\{x=(u,\lambda)\in\Re^n:\lambda\geq0\}$. $f$ and $g_i$ are all convex. ...

The above queries did not find any older occurrences. (After the next update of SEDE, this instance should be inluded there.)
 
 
5 hours later…
10:53 AM
Mar 13 at 9:07, by Martin Sleziak
Maybe there should be on meta. (Or some other reasonable tag name for this topic.) There are questions such as: Privilege page on reduced ads doesn't show on this site, even though there are now advertisements or What does the “see reduced ads” privilege mean?
Mar 13 at 9:07, by Martin Sleziak
And I have recently asked this one: Are there ads on Mathematics Stack Exchange?
 
11:14 AM
I created the tag on meta.
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Q: How to keep ads from appearing on stack exchange

coffeemathI find the ads about non-mathematical things annoying. I tried to click on one to report it but nothing worked. Is there a way a user of stack exchange can get rid of such ads? Some seem to appear for a few days and then go away, others then appear a few days later. Thanks for any information. Ad...

 

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