For a convex quadratic programming problem with the quadratic objective and linear inequality constraints. I had an example with 3 variables and 3 constraints. In the sample answer, we can solve them using the KKT condition to get the exact solutions.
Analytically, I think I can get the exact solution (global optimum) of the aforementioned optimization problems regardless of the question size using the KKT condition (or some other method, like the simplex method). But in tutorials, it said that it is very "expensive" to do so when we have large-scale convex quadratic programming problems. Instead, we use some numerical methods to solve them, usually, we set some tolerance for the objective function (for example, 10^−6).
My question is, how expensive it is if we want to get the exact solution (global optimum) of the quadratic programming problem I mentioned before? And how it relates to the number of inequality of constraints? Is it impossible to calculate it even with computers? I will really appreciate it if you can offer some references for this problem.
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