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seen Feb 9 at 9:40

Feb
9
comment How to prove that this function is convex?
Found some mistakes. Using a similar procedure as described in the previous comment proves concavity of $h(y)$ and so $f(x)$.
Feb
9
accepted How to prove that this function is convex?
Feb
9
comment How to prove that this function is convex?
I differentiated $h(y):=f(y/a)$ four times: $$h^{(4)}(y)=C \left(-e^y (y^2+5y+8) + 8e^{2y} \right) >8C\left(-e^y\left(\sum_{i=0}\frac{y^i}{i!}\right)+e^{2y}\right)=0,\,\,C>0$$ for all $y>0$. Then using $h^{(3)}(0) = 0$, it follows that $h^{(3)}(y)$ is strictly positive for $y>0$. This in turn implies convexity of $h''$. So no need to use sinh or cosh. Thanks anyway for the hint of replacing $x$!
Feb
8
comment How to prove that this function is convex?
I changed the title. Thanks for noticing.
Feb
8
revised How to prove that this function is convex?
changed error in title (concave => convex)
Feb
8
awarded  Scholar
Feb
8
asked How to prove that this function is convex?
Feb
8
accepted condition number after scaling matrix
Jan
28
asked condition number after scaling matrix
Aug
1
awarded  Tumbleweed
Feb
10
comment Optimal distribution with moment conditions
E.g., if $m_{n-1}=0.45$ and $m_n=0.45$ then the second point is close to $x=0.7$. Matlab code: N = 101; x = linspace(0,1,N); n = 5; x0 = zeros(1,N); x0(end) = .67; x0(round(0.65*N):round(0.75*N)) = .03; Aeq = [ones(1,N); L.^(n-1); L.^n];beq = [1; 0.45; 0.4];A = -eye(N);b = zeros(N,1); [x_opt f_val] = fmincon(@(p) -sum(p.*(exp(x)-sum((ones(n,1)*x).^((0:n-1)'*ones(1,N))./([1 cumprod(1:n-1)]'*ones(1,N))))),x0,A,b,Aeq,beq,zeros(1,N),[],[],optimset('Algorit‌​hm','sqp','MaxFunEvals',100000,'MaxIter',1000,'TolX',1e-32,'TolFun',1e-32)); plot(x_opt)
Feb
9
asked Optimal distribution with moment conditions
Nov
26
awarded  Supporter
Nov
26
awarded  Editor
Nov
26
comment surface unit sphere
@joriki: The norm bars are improved now.
Nov
26
revised surface unit sphere
minor change: I improved the spacing of the norm bars
Nov
26
awarded  Student
Nov
26
asked surface unit sphere