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 Dec28 accepted Find unknown matrix in matrix equation Dec27 asked Find unknown matrix in matrix equation Feb9 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 $f(x)$. Feb9 accepted How to prove that this function is convex? Feb9 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 $x$! Feb8 comment How to prove that this function is convex? I changed the title. Thanks for noticing. Feb8 revised How to prove that this function is convex? changed error in title (concave => convex) Feb8 awarded Scholar Feb8 asked How to prove that this function is convex? Feb8 accepted condition number after scaling matrix Jan28 asked condition number after scaling matrix Aug1 awarded Tumbleweed Feb10 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) Feb9 asked Optimal distribution with moment conditions Nov26 awarded Supporter Nov26 awarded Editor Nov26 comment surface unit sphere @joriki: The norm bars are improved now. Nov26 revised surface unit sphere minor change: I improved the spacing of the norm bars Nov26 awarded Student Nov26 asked surface unit sphere