A function f:R^n \to R is logarithmically concave or log-concave if f(x)>0,\forall x\in dom f and \log f is concave,for a log-concave function f,we have f(\theta x+(1-\theta)y)\geq f(x)^\theta f(y)^{1-\theta},\
geometric mean/ A0230 Function theory, analysis A0240 Geometry, differential geometry, and topology B0220 Mathematical analysis B0250 Combinatorial mathematics C1120 Mathematical analysis C1160 Combinatorial mathematics E0210C Mathematical analysis E0210E Combinatorial mathematics...
log-convex function 的和还是 log-convex function 简单证明？其实Boyd的书里提过这个，在3.5.2节。...
Thereforep(aN|tN)p(aN|tN)is log concave not log convex, since the logarithm ofp(aN|tN)p(aN|tN)is concave. A log convex function is also convex, so ifp(aN|tN)p(aN|tN)were log convex it would also be convex which doesn't make sense since it is a probability distribution and it ...
The authors study log-convexity for matrix functions and consider the gamma function in this setting. They also consider the notion of log-convexity on the positive cone of positive continuous functions. A criterion for log-convexity is obtained in both cases.Reviewer: Tatjana Ostrogorski (Beograd...
Illegal operation: log( {convex} )” that is because of the term inside the \log, \sqrt{\alpha}, which is a convex function. How can I reformulated the objective in a way that Disciplined convex programming be satisfied? Many thanks in advance for any tips and hints!Mark...
The second part which has the -log function is certainly concave. In conclusion, this constraint is convex. But when I use cvx, it always says: Illegal operation: log( {convex} ). I understand that in cvx, we should make sure the formula within the log function should be concave. But...
( 3 ), some classical inequalities can be obtained through special log-convex function. in addition, these inequalities have a very significant role for log-convex functions in both pure and applied mathematics. jensen’s inequality [ 11 ] is one of these inequalities for convex functions, ...
We suppose that the cost function is quadratic and the demand is a convex and log- linear function. The game is modeled with a system of two difference equations. Existence and stability of equilibria of this system are studied. We show that the model gives more complex chaotic and ...
The function MSVCRT - memcpy if the fastest but, according to MSDN, it can’t be used for overlapping data. Otherwise Array.Copy and memmove are identical with a very consistent but negligible time advantage for memmove. To use memcpy, we require to copy the entire array each time (same ...