Can this be changed to a convex problem? If I have a problem that is not convex
\begin{array}{lll}
\textbf{P1:} & \min_{\alpha,q} & \alpha q  \\
&\text{s.t} \quad &\alpha \leq 1    \\
&&\alpha \log_{2}\bigg(1+\dfrac{q}{\sigma^{2}}\bigg)\geq 5\\
&&\alpha \geq 0    \\
&&q \geq 0  
\end{array}
I think its noncovex because of the second constraint. I want to know how can I change such problems into convex. Any reference of book, slides, lectures, articles or name of a technique would be helpful. Also kindly name some techniques for nonconvex optimization like ant colony optimization etc. I would prefer if the reference is not of a book as I cannot buy books online and their is a fair chance that the hard copy of book will not be available in my county. 
 A: Please forget about ant colony optimization. Its a heuristic with unpredictable performance.
Making problems convex is an ad-hoc procedure that requires practice.
The objective is the first hurdle here. It is indefinite. A logarithmic transformation gets rid of the product, but results in a concave minimization problem. We can make the objective linear again with the substitution $x=\exp(\alpha)$ and $y=\exp(q)$. Let's see what happens to the constraint:
$$\log(x) \log(1+\log(y)/\sigma^2) \geq 5$$
$$\log((1+\log(y)/\sigma^2)^{\log(x)}) \geq 5$$
$$(1+\log(y)/\sigma^2)^{\log(x)} \geq \exp(5)$$
$$1+\log(y)/\sigma^2 \geq \exp(5)^{1/\log(x)}$$
Here I used that $\log(x)\geq 0$. The final constraint is convex as $x \geq 1$. Finding an initial feasible point is slightly harder since the constraints are not convex outside the feasible region, but for this two variable problem that is not a real issue. The final problem becomes:
$$\begin{align*}
\min \quad  &x+y \\
\text{s.t.} \quad & x \leq e \\
& 1+\frac{\log(y)}{\sigma^2} \geq \exp(5)^{1/\log(x)} \\
& x,y \geq 1
\end{align*}$$
