549 reputation
214
bio website opentox.ntua.gr
location Athens, Greece
age 29
visits member for 3 years, 8 months
seen 2 mins ago

1h
asked Series in closed form
Nov
2
comment Convexity of a function
There are a few facts that may help you (although, I believe you need to rephrase your question to make it more clear). First, if $P$ is affine, i.e., $P(x)=Ax+b$, and $G$ is convex, then $F$ is convex. Second, assume that $P$ is given by $P(x)=(P_1(x),\ldots, P_n(x))$ and each $P_i:\mathbb{R}\to\mathbb{R}$ is convex. Assume that $G(z_1,\ldots, z_n)$ is nondecreasing in each $z_i$ (when other variables are fixed) for each $i$. Then $F$ is convex.
Nov
2
comment convex set but not convex cone
Firtly, a convex set need not contain a cone. Maybe, you wanted to say that a convex cone is a particular instance of the family of convex sets. As @QuangHoang said, open (and closed) balls are not cones. Then, any nontrivial (not the set $\{0\}$) compact convex set is definitely not a cone.
Sep
15
comment Ellipsoidal Decomposition: Finding ellipsoids whose sum contains a given ellipsoid
I'm not sure it is very clear; for example, what do you mean by The area of these ellipsoids is related by a linear cost variable? Otherwise, you are looking for a set $Z\triangleq X+Y$, where $X$, $Y$ are ellipsoids and $Z\supseteq E$. Why not choosing $X=\{0\}$ (which is trivially an ellipsoid), $Y=E$? (in this case $Z$ becomes a minimum volume outbound ellipsoid for $E$).
Jul
2
awarded  Curious
May
13
awarded  Tumbleweed
May
6
asked Kakutani's FP theorem for $F:X\to 2^Y$
Oct
12
awarded  Critic
Oct
5
revised Polytopes inside polytopes
Another criterion added - update
Oct
5
revised Polytopes inside polytopes
Another criterion added - update
Oct
4
revised Polytopes inside polytopes
added 435 characters in body
Oct
4
revised Polytopes inside polytopes
deleted 57 characters in body
Oct
4
answered Set of all affine maps between two polytopes
Oct
3
revised Polytopes inside polytopes
added 708 characters in body
Oct
3
asked Polytopes inside polytopes
Oct
3
revised Implications of $\|Ax\|_1\leq \|Bx\|_1$
deleted 4 characters in body
Oct
3
revised Implications of $\|Ax\|_1\leq \|Bx\|_1$
update
Oct
3
revised Implications of $\|Ax\|_1\leq \|Bx\|_1$
Update - answer.
Oct
3
revised Implications of $\|Ax\|_1\leq \|Bx\|_1$
added 2 characters in body
Oct
3
asked Implications of $\|Ax\|_1\leq \|Bx\|_1$