PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (236)
Orphanage
Unclass'd (1)
Unproven (540)
Corrections (46)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Copyright
About
Forum: Competition Questions
Welcome to the Competition Questions forum!
For discussing problems from mathematics competitions.

[ back to forums top ]
Discussion
Style: Expand: Order:
forum policy

jump to page: 1 2 3 4 5 6 7 8 9 10 >> of 10 (49 items)

convexity by ercanatam on 2009-08-02 21:56:09
Consider
\begin{align}
\dot{x}=A(p)x+B(p)u
\end{align}
where $A(p)$ and $B(p)$ are linear in the fixed-parameter(but unknown)vector $p$.
The solution of the above problem is
\begin{align}
x(t,p)=e^{A(p)t}x_{0}+\int_0^te^{A(p)(t-\tau)}B(p)u(\tau)d\tau
\end{align}
Assuming that experimental data $x_e$ is available at time points $t_1,t_2,\cdots, t_N$,
the objective is to minimize
\begin{align}
f(p)=\sum_{i=1}^N\left|\left|e^{A(p)t_i}x_{0}+\int_0^{t_i}e^{A(p)(t_i-\tau)}B(p)u(\tau)d\tau-x_e(t_i)\right|\right|^2
\end{align}
Let
\begin{align}
f_i(p):=\left|\left|e^{A(p)t_i}x_{0}+\int_0^{t_i}e^{A(p)(t_i-\tau)}B(p)u(\tau)d\tau-x_e(t_i)\right|\right|^2
\end{align}
Then,
\begin{align}
f(p)=\sum_{i=1}^N f_i(p)
\end{align}
Since sum of convex functions is convex, to show that $f(p)$ is convex we have to show that
$f_i(p)$ are convex.
\\\\
\textbf{Question}: are $f_i(p)$ convex?
[ reply | up ]
Gamma Distr by georgiosl on 2008-12-31 09:00:23
sum of ind random variables X_i - G(x,a_i,b_i) is Gamma distr and parameters?
[ reply | up ]
A question on continued fraction expansion by Carlton on 2008-10-21 02:19:48
Let $\alpha_j=G^j(\alpha)$ is the j^th fractional part in the continued fraction expansion , where $G$ is the Gause map: $x\map {1/x}=1/x-[1/x]$. If there is such fact that the product $\alpha_{n-1}\cdot\alpha_{n-j}$ is no large than $2^{-j/2}$, for any ( or sufficiently large) $n,j$?
[ reply | up ]
Prove the unicity of Lebesgue measure. by Onezimo on 2008-10-12 13:43:59
Can somebody helps me with this problem?
[ reply | up ]
are polynomials dense in C(R)? by mohsenz90 on 2008-05-28 23:56:29
Is the following statement right?
for every continuous function like f,there exist a sequence of polynomials like P_n which P_n -> f
[ reply | up ]

jump to page: 1 2 3 4 5 6 7 8 9 10 >> of 10 (49 items)

Interact
post