Objective Function of Maximum Margin Classifier is Convex. How? How one can prove that Objective Function of Maximum Margin Classifier(MMC) is Convex in LP or QP?
I've searched through the internet where derivation of objective function is provided and it says we know that f is convex but how it is convex? like in this link (http://svr-www.eng.cam.ac.uk/~kkc21/thesis_main/node12.html)
But can we mathematically prove that objective function of MMC is convex?
 A: These are two questions in one. Or maybe I don't understand which of the two questions you are asking.
1. Is a maximum margin classifier a QP ?
A QP is a problem of the form:
$$ \text{minimize }\text{ }    x^TQx+p^Tx \text{ }\text{ subject to }\text{ } Ax = b, Cx \leq d  $$
With $Q$ a definite positive matrix. Depending on the source or specific problem you are considering, you only need to convince yourself that the optimization problem can be written under this form.
2. Is a QP a convex problem ?
Yes, a QP is a convex problem. Indeed, a convex problem is an optimization problem of the form:
$$ \text{minimize }\text{ }    f_0(x) \text{ }\text{ subject to }\text{ } Ax = b, f_i(x) \leq 0 $$
with $f_0$ and $f_i$ convex functions.
In our case: 


*

*$f_0(x) = x^TQx+p^Tx$ , hence the hessian of $f_0$ is $\nabla^2_xf_0 = Q $ which is positive definite, so it is a convex function.

*$f_i(x) = Cx-d$ are affine functions, hence convex


So a QP is a convex problem.
Further reading
For a well formalized and thorough mathematical framework on convex optimization, you can refer to this excellent course from Alexandre D'Aspremont http://www.di.ens.fr/~aspremon/OptConvexeM2.html
You will find there a clear definition of different optimization problems, and a toolbox for proving the convexity of problems.
