What is the main idea of the Inner Approximation Optimization algorithm?

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I see that there is an optimization method which is called inner approximation that is

Technical Note—A General Inner Approximation Algorithm for Nonconvex Mathematical Programs

But since I am quite new to the field of mathematical optimization, I am not sure what does this term "inner" imply.

Some research paper actually use this method to approximate the solution for their non-convex problem but I still not get the gist of it, an example would be this paper

Joint Rate and Power Control in Wireless Network: A Novel Successive Approximations Method

From this paper point of view, this method locate the solution of non-convex problem in an iterative manner as long as some properties are satisfied.

Any help is welcome and a simple example would be quite nice.

Could anyone kindly please explain this to me, thank you very much for your enthusiasm !

Edit: There are two algorithm that is both called Inner Approximation:

The first one is in the Technical note above

The second one belong to Hoang Tuy's global optimization which is also called the polyhedral annexation method