How to check whether a Stochastic Model Predictive Control (SMPC) based Optimization Problem is Convex or Not?

I am trying to solve a stochastic model predictive control based optimization problem. Is there any function or subroutine in matlab that could help me evaluate whether the given optimization problem is convex or not?

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Theorems have proofs. If the theorem says that the problem is convex, there should be a proof for this assertion. So why using MATLAB for this task ?
Actually I have simulated this theorem using YALMIP-SDPT3 with MATLAB and I have used built-in 'norm' function to calculate norms in simulation.
What I have been able to understand from a reply of Dr. Johan Loferg to my query in google forum for YALMIP, 'norm is not convex by propagation', so, I need to design my own norm calulation function...
I want to establish convexity of my optimization problem through some alternative means...
Here is the link to my query : Query

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