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I'd like to start by clarifying I'm by no means an expert in any of this, so take everything I say with a grain of salt.

Convex and Non-convex Optimization are subfields of mathematical optimization that focus on minimising convex and non-convex functions respectively. That is, finding the global minimum of functions with one or multiple minima.

Quadratic programming is also a subfield of mathematical optimization that also focuses on minimising convex and non-convex functions.

Convex and Non-convex Optimization seem to focus on quadratic functions, Quadratic programming also focuses on quadratic functions.

I do understand the difference between convex and non-convex optimization, but I'm having trouble understanding how quadratic programming fits into all of this.

I tried Googling my question in several different ways with no luck. I searched this website and it seems this question has never been asked before.

Is there an area of mathematical optimisation that quadratic programming doesn't cover? If there is, I can't seem to find a single example. If there isn't, it seems very odd to me that quadratic programming is differentiated enough that it has a completely separate name and Wikipedia page.

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  • $\begingroup$ Quadratic programming does not cover linear programming, for example. I do not understand your question $\endgroup$ Jun 4, 2023 at 6:19
  • $\begingroup$ @RodrigodeAzevedo I've never heard of Linear Programming until now, and that answers my question. My confusion came from the fact every example I've seen of mathematical optimization I've seen so far has been a quadratic function. $\endgroup$
    – Vee Amona
    Jun 4, 2023 at 6:43

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No, quadratic programming does not cover all optimization problems. Quadratic programming is limited to the case where the objective function is quadratic and the constraints are linear functions.

If you have an optimization function where the objective function is not quadratic (maybe it is cubic, or maybe it is some other complicated function), or the constraints are not linear functions (maybe they are quadratic or some complicated function), then that is not an instance of quadratic programming.

There are convex/non-convex functions that are neither quadratic nor linear.

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