Problem formulating a Min-Max problem in CVX

I have the following max-min problem and I am trying to formulate it in CVX.

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I have re formulated the problem to make it a standard convex optimization problem as

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but I am not able to write the first constraint in CVX, I have to take t as another cvx variable(along with p and c, rest are constants).I have tried writing the constraint in many ways but CVX wont take it(t,c,p are variables the constraint is violating the multiplication rules of CVX.) HELP!!

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Data file:
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Is the problem convex? It does not seem so. If so, CVX can’t solve it, and no amount of rewriting will change that.

Indeed, as mcg suggests, the Hessian of the first constraint is indefinite, hence not convex.

Sir, if the hessian is indefinite for few of the points, does that means that the constraint and the problem is non convex altogether?
can I find a convex set(bound the values of my primal variables, p t and c), such that the eigen values of the hermetian part of the hessian matrix is positive for…

those values…and so, that part of the problem is convex. can I take the Lagrangian, and solve for it?

CVX is not used this way. It is only for problems that can be built according to the strict rules laid out in the documentation. Allow me to suggest that your modeling approach is not compatible with CVX, and you may need to look for another tool.

Please refer to this answer to understand why your attempts to use CVX in this manner are going to give you nothing but frustration: Beginner’s question#1161