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saddle point problem, interior point algorithms and convex approximations?

Can anyone explain what is a saddle point problem and what is its context in fluid structure interaction computations? I am from mechanics background and was currently reading a Local maximum entropy approximations by M.Arroyo for my research work. I couldnt understand the context of Local Maxent part, as the notations are difficult to understand and it will be easy for me understand the mathematical expressions more clearly if I could understand the physical context. I would really appreciate if anyone could explain me this or give some reference materials to feed my brain with more physical contexts of these problems rather with just equations.. ? 

Thanks

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