2
votes
0answers
49 views

Problem reduced to analyzing solutions of a family of nonlinear systems of equations

This was posted on mathoverflow about two weeks ago and I got no response so I'm asking here in case anyone has any ideas. Original post is here. I was able to reduce a research problem relating to ...
1
vote
1answer
287 views

Two Concepts of Monotonicity

Let $K$ be a closed convex subset in $\mathbb{R}^n$ and $F: K\rightarrow \mathbb{R}^n$. We say that $F$ is strongly monotone on $K$ if there exists $\gamma>0$ such that $$ \left<F(y)-F(x), ...
5
votes
1answer
138 views

An absolute value inequality question

It is well-known that, $\left|m-n\right|\ge\left|\left|m\right|-\left|n\right|\right|$ for real numbers. But if one defines $\left|M\right|=\sqrt{M^2}$ for a symmetric matrix $M$, does one have ...